You picked a good character! Always happy to see a new Doc main.
Offstage
Back air There's not a lot that leads into a back air offstage, so this is the simplest move in his edgeguarding kit: if your opponent is in range for a back air and it'll gimp or kill, back air them. The only setups I can think of is rising back hit up air -> back air at around 50%, but since that uses your double jump, it's risky.
Up air Up air is fast, has pretty decent vertical range by Doc standards, and sends opponents at a nasty angle. The horizontal hitboxes of up air are a bit weird and take some getting used to, but to simplify it: if you're hitting with the front hit, try to position yourself so that you're slightly below where the opponent will be. This is because the up air hitbox hits in a more diagonal area. If you're hitting with the back hit, try to position yourself so that you're level with where the opponent will be. This is because the back hit takes longer to come out.
Down air There are lots of places where you can learn to spike and I don't think Doc goes about spiking particularly differently, except that he's more limited in how he can use it since his range is so short and he can't go very deep at all. What I will say about Doc's spike, though, is that the hitbox extends surprisingly far. It's basically a downwards back air with more startup.
Maybe I'm just bad at using it, but I rarely get any spikes. It's good for securing early kills and punishing ledge regrabs, but most of the time I feel like I could be using any other option. But except against characters with insane recoveries like Villager and Snake, it'll almost always kill if it lands offstage.
Neutral air A pretty underrated option if you ask me. While the initial weak hit isn't good, it's thankfully a small part of the move. The strong hit has surprising launching power and a good angle, and it's the majority of the move. (I'd post the exact frame data, but I don't know it offhand.) You can use it as a lingering hitbox when you've cut down your opponent's recovery options to one single option and other things like down air and down B aren't available, or throw it out as a mixup if you read their recovery.
Forward air I don't often use this as an edgeguarding option, but it's very powerful if you read a jump. Be cautious of how much endlag the move has, since you can make some situations unrecoverable if you use it badly.
It's worth mentioning that if you fair off the ledge, buffer a jump (holding the jump button is a good idea), and then angle an up B upwards (done by moving the analog stick to the opposite direction your character is facing after inputting the up B), you can make it back consistently. It's still incredibly risky since it's a somewhat tight series of inputs and it's literally your only option, so you can also get gimped consistently. But it looks really cool and feels amazing to pull off!
Neutral special It's mediocre at gimping on its own (but can catch low recoveries if they use their jump at the wrong time, or mess with recoveries like Ike or Cloud's), but where its real strength offstage lies is in the traps it creates. When you aim a pill offstage, you're essentially creating a small zone where someone's recovery plan will be suddenly halted if they cross it. So it limits their options: if they cross it, it won't kill, but it does give you some more time to edgeguard them. If they don't cross it, that's one less potential recovery path for you to worry about.
And of course, just like onstage, you can use neutral B offstage to get followups if you follow the pill you throw out. Up air and down B are the best ones here.
Side special You can use this to flip any telegraphed recoveries, or throw it out anywhere, really, and seriously trip up your foe. A nice advantage is that since Doc falls while using the move, it's a little easier to hit opponents below you - if they stall their recovery and time it to avoid the cape, you might fall into them and cape them anyway. I feel that this is a situational edgeguarding option, since the move takes a while to come out. I only tend to use it out of combos that began onstage to add pressure, or when someone keeps doing the same recovery.
Down special This is probably my most used edgeguarding option. It's a great option against high and low recoveries, and there's all kinds of ways you can move around with it: you can rise up and cover a long range vertically and horizontally, you can stay in one spot (e.g. the ledge) and be a huge obstacle, or you can drop down really fast to catch low recoveries. And, it honestly kills so early that I'm scared it might get nerfed. Seriously, it's good.
If you catch your opponent from around the middle of the move, keep this in mind: for the first half of the move, move in the direction opposite of the nearest blast zone, and then in the second half, move towards the blast zone. Moving away makes sure the opponent doesn't accidentally get caught in the other side (where they'll be launched onto the stage), while moving towards helps kill a little earlier.
How you should move exactly depends on where the opponent is relative to you, but what I said is a good rule of thumb. You'll learn through experience.
Up special This isn't so much a specific edgeguarding option as it is just a quality of the move coming in handy, but you can use it to your advantage. If someone has weaved around your edgeguards and is going for a low recovery, you can catch them with an up B and stage spike them. The move is frame 3, making it among the fastest aerial options in the game, so it's extremely hard to challenge if you time it right (and timing it is easy since it's essentially just reacting to their up B). It also has enough knockback that it's untechable at high percents.
This move is also especially useful in some matchups like Villager and Meta Knight, since the inconsistent freeze frames of Villager's balloons in relation to when it hits them can seriously throw off the Villager player, and Meta Knight does a loop that puts him in place for up B twice, while the sword hitbox faces the other way.
Also, learn your magnet hands! Doc has an amazing ledge grab range just like he did in Smash 4 and knowing this will help you feel safer offstage.
Using your jump Like you touched upon, it's risky for Doc to try edgeguarding, because if you make a mistake, you will lose your stock regardless of percent. It's important to treat your jump like a last resort and a safety net - it's much more versatile than your other recovery option, down B, so whenever you use it, be sure you know exactly how you're going to get back to the stage and don't hesitate to get back there. Better safe than sorry.
As a rule of thumb, if you're not entirely offscreen and you're at least slightly above level to the ledge, a recovery is usually possible (theoretically possible - nothing is stopping your opponent from edgeguarding you) so long as you have either your jump or your down B. Doc's recovery is a bit better than people give it credit for, although it's still not good.
Ledge
Forward tilt When angled down, this is Doc's most reliable two framing option. Quick, decent angle. Make sure that the shoe hits off the ledge rather than on it, since most characters have two frame animations that put them away from the ledge horizontally.
Dash attack This is a good tool for keeping pressure on the ledge. It hits slightly below the ledge and stays out for a while, so if your opponent is getting too comfortable on there and burns out their invincibility, you can dash attack them and put them in a vulnerable situation. Keep in mind, though, this only works if the character's ledge grab animation puts a hurtbox high enough. You won't be able to hit characters like Palutena with a dash attack. It can also intercept recoveries without hitboxes like Rosalina's and Inkling's if they don't play around your dash attack.
Unfortunately, you won't be getting kills off of this very often since only an up air is guaranteed at most percents (at lower percents, you can get a non-lethal back air), and that doesn't kill at the ledge until insane percents (the same percents it stops being true out of dash attack), but you can try to read how they react to it.
Down tilt Similar to dash attack, though not nearly as good. It'll only be able to hit characters with especially bad ledge grab animations that put a huge hurtbox high above the ledge, like Ness and Lucas. However, the lower position of the opponent means that you can get quite a lot off it, like up air, back air, up B, and down B.
Up smash By far the best option on the ledge. There's so much good about it! It kills early, it can cover all options besides getup attack with the right timing, it's so fast that you can sometimes just up smash again if they roll past it, and it's noncommittal. Be sure to face away from the ledge and mix up your spacing: the closer you are to the ledge, the more you'll cover jump getup. The farther you are, the more you'll cover roll getup, ledge attack, and ledge drop aerial. (For ledge drop aerial specifically, I recommend facing towards the ledge as well to get your hurtbox away from their attack.) Up smash is also very good at challenging aerials from above since the head has intangibility.
Down smash This smash is frame 5, which is faster than some characters' jabs, and it sends opponents at a nasty angle. Like dash attack and down tilt, it hits slightly below the ledge. If your opponent makes an impatient landing or ledge getup, or whiffs an attack, you can do a down smash. The only problem with it is that it doesn't kill that well on its own (middleweights die on the ledge at around 110%) and it's pretty laggy, at least by Doc standards. This move is best against characters like Ganondorf and Donkey Kong that have limited options when recovering from semispikes.
Down B I use this on the ledge only as a mixup. If you predict when your opponent will get up from the ledge, using down B and moving away from the ledge covers neutral getup and roll getup simultaneously: the large hitbox of down B will catch the opponent even when moving away(unless they're a very skinny character like Wii Fit), and the move lasts long enough that the final hit will outlast their roll invincibility. Up smash generally does this better, but it can throw off the opponent or can be used if up smash is stale.
