Added this to my OP:
Shulk's neutral
So, we all know what the neutral is. This is basically and honestly the most important state you need to know because how you play at the neutral will determine whether if you'll be at the advantage or the disadvantage. Smash 4 is very neutral heavy. Don't be surprised if you find yourself in this state in matches. You're going to find yourself having to win at the neutral over and over AND OVER again (if you're good enough), but whatever. Now, let's take a look at Shulk's neutral.
Now, Shulk's options at neutral vary a lot depending on his arts. His arts are made to respond to the situation he's in. Say, if he has to deal with projectiles, his go-to art would be jump and speed. If the opponent is trying to break into his zone, he can either use buster art and attempt to keep the opponent at bay, or he can use speed and jump to stay mobile such that he can keep himself away from the opponent if ever he or she gets too close to Shulk. He can also use shield and take the hit then punish the opponent for actually hitting or even throwing Shulk at low to mid percentages. Your arts will be used for specific situations. You should see them as tools when it comes to dealing with match-ups but there are those times where you need to maximize your utility of the art you're currently using depending on the situation. Shulk's playstyle ultimately is all about footsies/mid-range, unless you're in smash art, in which case, you shouldn't use it at all in the neutral unless you're trying to go for the read.
Knowing Shulk's poking options with each of his arts are extremely important, even in shield and that art decreases Shulk's damage output. Anyway, Shulk's range is amazing. Yeah, you get it. We all get it. Your opponent probably gets it. Abuse it. Use it to your advantage and space the **** out of your opponent. You do not want your opponent to get any closer to you because Shulk's CQC is utter crap. How do you keep them away? What moves do I use with Shulk?
In vanilla
- B-air is pretty safe on shield if well-spaced, if you hit it up close on shield, you're ****ed
- Retreating n-air (tipped) is safe although it requires precision to land
- D-tilt is relatively safe on shield although landing it up close on shield will get you wrecked
In speed
- Retreating b-air is safe on shield
- Retreating FF f-air is safe on shield
- Retreating n-air is safe on shield
- RAR tipped b-air is safe on shield (?)
In shield
- Retreating tipped n-air is safe on shield
In buster
- Retreating f-air is safe on shield
- B-air is safe on shield
- Tipped FF n-air is safe on shield
- F-tilt is safe on shield
- D-tilt is safe on shield
- F-smash (possibly) is safe on shield if tipped (?)
In smash
- Nope
So yeah. Those are his options with footsies. Just balance it and mix it up between tilts and aerials. Make sure you aren't predictable with your footsies or the dash to shield grab will happen when they find your obvious patterns. Before I move onto mobility, I'd like to make a special mention for u-tilt because of its amazing vertical coverage. It's great for covering aerial/vertical approaches so take note of that! With buster art, you can even chain u-tilt repeatedly!
Mobility is also an important aspect when it comes to the neutral. As mentioned earlier, mobility is important for mixing up your movement against your opponent. With speed, you can dash dance, dash to shield, jump back and forth, very well while sticking close to the ground while abusing SH n-air, b-airs, pivot f-tilts, and pivot grabs. With jump, the whole stage is basically your playground. You can jump around like an idiot, confuse your opponent with your sheer mobility, perform tomahawks, use n-airs in mid-air or f-airs to gain coverage or catch air dodges, etc. etc. You get the point. Mobility is an amazing tool in Smash Bros. Try it out. Learn how to apply it and abuse it in certain situations
Also, make sure you take note of MALLC. MALLC is a crucial and must-learn tech for Shulk mains since executing it successfully will cancel the landing lag from Shulk's aerials. This is really important in Shulk's neutral since it does and can potentially do the following:
1) Maintain mid-range dominance with the rapid use of MALLC b-air
2) Punish opponents for punishing MALLC
3) Combo'ing into f-tilt, f-smash, jab or dash grab after canceling landing lag
Oh, and yes. MALLC has invincibility. Well, art activation animation already has intangibility to begin with but the window varies depending on which art you use. You still need to space with MALLC though because landing up close with MALLC will still get you punished. Hit with the middle part of the aerial to maximize MALLC's potential
If you ever find yourself feeling like you're on the brink of being at a disadvantage, use jump or speed (mostly jump art) to escape or use shield and take the heat if you think the damage won't be that much. Shield is kinda useless though against those characters who already hit hard to begin with (Bowser, Ike, Ganon, Falcon... sort of, D3, Zard, etc.)
Now Shulk's primary issue in the neutral is the fact that his attacks have commitment. This is easily noticeable especially when you look at his beautifully atrocious frame data. Yeah, there's that. Take note that his attacks have lag so make sure you make the most out of your monstrous range. There's that, and also against defensive opponents with a patient mindset, you'll be forced to approach and Shulk doesn't like to approach. When this happens, just stay away from close-range and stick to mid-range harassment. Shulk is hopeless at CQC (well... almost)
Shulk's advantage
When do you know if you have the advantage? Well, it's quite simple really. If you have the opponent in a combo, if you're opponent is hanging on the ledge, if you opponent is down on the ground, if the opponent is above you, if the opponent is off-stage and trying to recover, and if the match's pace is basically being dictated by you. Shulk's advantage is AMAZING. He gains so much profit from jump art and buster art, most notably. Smash art is also the art to go-to once you have your opponent in a disadvantageous position. Speed art is also decent at advantage due to it having a good number of strings and combos (thanks to its augmented mobility) but the damage is lackluster and unlike jump, your combos are more limited due to your shortened jump height. Even shield art is useful at this state. You can dictate the pace of the match and turn it into a slow crawl by being a defensive *****. The advantaged state can appear in many forms but truth be told, each situation in this state can be optimized depending on a certain set or just one art.
For example, an opponent off-stage trying to recover? Nice! An edgeguarding opportunity! Jump art and smash art are the optimal arts for edgeguarding. Jump art's increased recovering capabilities allow you to go in deep without any fears of self-destructing. Your options while edgeguarding in jump art are f-air, d-air and b-air, although f-air is much more notable, precise and easier to use but anyone can react to it if you're too predictable. Learn how to condition and mix up your movements. Shulk falls fast so you don't really have that much time to think while staying off-stage. With smash art, the increased knockback basically insures death even at surprisingly low percentages (~60-70%). It's a lot easier to aim since you fall slower and n-airing off-stage isn't really a bad idea. Plus, you can even catch air dodges with n-air! You can't really go far though because unlike jump art, Smash art does not augment your recovering capabilities so don't get too crazy.
As far as combos go, landing d-tilt, n-air or d-throw will allow you to follow up very well and rack up a lot of damage but that's detrimental on which art you're using. Buster art, speed art, and jump art are the notable arts when it comes to combos. Buster art combos are incredibly potent and deadly. So deadly, you can rack up an easy 35% damage in 2 hits, and if you land the tighter strings, you can easily rack up ~56% damage or even more than that. It's all thanks to the lowered knockback. With jump art, from ~30%+, you have the potential to basically take the stock from the opponent if you manage to sweep them off-stage with some f-airs. Speed art is basically functions like jump art but it has less combos and it even deals less damage. Speed art combos are good for setting the opponent in a certain position, or in other words: "Speed art combos are good for setting up."
Some notable follow-ups/strings/combos (some are DI/reaction based):
Jump art (N-air > F-air > F-air)
Jump art (D-tilt > F-air > F-air)
Jump art (D-throw > F-air > F-air)
Jump art (N-air > U-tilt > F-air > Air slash)
Jump art (N-air > F-air)
Jump art (N-air > B-air)
Jump art (N-air > D-air)
Buster art (N-air > F-smash)
Buster art (N-air > F-tilt)
Buster art (N-air > d-throw > F-smash)
Buster art (N-air > d-tilt > d-throw > F-smash)
Buster art (D-tilt > D-tilt > D-throw > F-smash)
Buster art (D-tilt > D-throw > F-smash)
Buster art (B-throw > Back slash)
Speed art (N-air > D-throw > F-air)
Speed art (N-air > B-throw > Back slash)
Speed art (D-tilt > F-air)
Speed art (N-air > F-air > F-air)
Now we're done with the combos, let's talk about Shulk's ledge trapping.... It's amazing. It doesn't matter which art you're using but... if you want to rack up damage, use buster when ledge trapping? If you want to KO, use smash. If you want to set up for an edgeguard attempt, smash or jump art works. If you want to have an easier time ledge trapping, use speed because sliding u-smashes and RAR b-airs are great for covering options from the ledge. Pretty much almost all of Shulk's moves are amazing for ledge trapping. The only moves that aren't good for ledge trapping are u-air, d-air, back slash, air slash (due to it being HORRIBLE on whiff), and counter. All his other moves are seriously good for ledge trapping. Most notably, speed art sliding u-smash and u-tilt. You can rack up so much damage with buster just from keeping up the ledge pressure and you can even land the KO with smash art u-tilt or u-smash or f-smash or d-smash. It's all goooood
Shulk's disadvantage
Oh god. This one. Shulk's physical attributes basically make him combo meat in every art sans smash art and shield art. This is one of Shulk's main weaknesses and that isn't the only reason why his disadvantage is pretty bad. His recovery without the help of jump art (and a bit of speed art) is easy to gimp. It's not bad for recovering but it is definitely easy to gimp since it doesn't ledge snap instantly. Knowing how to escape the disadvantaged state is extremely crucial with Shulk because if you don't know your options at the disadvantage, your ****ed and **** can go south reeeeal fast.
Shield art is basically your best panic button for this. You take less damage and you even get the chance of escaping the combo early since you take significantly less hitsun while being in shield art (thank you based defense buff and weight buff!). Also, take note that you should STAY AWAY from this art if you're near the ledge of the stage. Your opponent will most likely attempt to throw you off-stage. Anyway, one more thing about shield. If the tendency of your opponent is to run from shield art, take advantage of that habit and use shield art. They'll run and try to camp you out thus you reset back to the neutral state
Jump art is your go-to art for escaping juggles and recovering back on-stage. With jump art, recovering is MUCH MUCH easier and your vertical recovering ability is godlike. Your jump height is increased and your air mobility is amplified so you can take advantage of that when it comes to getting around edgeguarding attempts (FH air dodge, etc). With regards to using it against juggles, you basically jump away and use your air speed to escape. So yeah. Be careful though with jump, because you take more damage. As in, +22%. That's quite a lot of additional damage you're taking per hit...
Final words
In the end, the best way to handle the 3 states is to know your opponent and the mechanics of the character the opponent is using. Once you learn the opponent's mechanics, determine which art is optimal when you're in a situation wherein the opponent is attempting to exploit a certain mechanic/set-up against you. Should you use jump to jump away? Should you switch to smash and take more knockback to get out much faster? Or use shield and take the hit and punish them? Treat the arts as tools. Maybe there will be times wherein you can treat them as other ways on how to deal with situations (i.e: playing mid-range ALL THE WAY with jump/speed/buster). It really depends. Shulk is a dynamic character and we all have different methods with playing the character
So yeah. Feelin' it