This is coming from someone who hasn't played Melee since Brawl came out, and has only tried PM once. I've not played competitively until Smash 4, so I may not be able to give great advice on whether he's a great choice coming off of those guys. I do find him to be a really fun character though, once you can get around his Monado Arts, and what to use when. It really alters the way you should be playing him, so it's he's good for a bit of variety like that.
You'll probably already have a rough idea of how the Arts are used, but I'll go through it anyway. Jump is almost exclusively used for recovery or edgeguarding. The deterrent is that the x1.22 damage you take. On-stage you can play it a bit hit-and-run, just don't get shield-grabbed. He has some really flashy (often sacrificial) true combos in Jump that guarantee a KO - carrying them out into the blast line and using Air Slash to seal the deal. Hype as hell when pulled off. Speed is can be hit-and-run as well as just chasing people down. Pivot grabs, following aerial opponents (Speed's walk is faster than regular's run), low% combos are amazing. Shield is Shield, enough said. Can sometimes be used if you want to hold your ground near a ledge. Buster's damage output (x1.4) is absolutely mental. The reduced knockback isn't really a drawback because you can combo for longer. Space yourself really well, shield damage and pushback is great, the extra damage taken (x1.13) isn't too bad. Smash is exactly what it looks like. I find it hard to use because it announces your intention to KO them. But you can get some great KOs if you make a good read here.
Generally speaking, expect to have a great time fighting large characters, expect to have a tough time fighting fast characters and some projectile-users. Jump and Speed are your best friends against them but they can't always be active and over a longer period the drawbacks start to hurt.
Dtilt, ftilt, nair, fair and bair can all be used for spacing to various degrees of quality. KO moves would be all smashes, ftilt, utilt, uair and dair. Utilt beats most, if not all aerials in a challenge. Shulk's aerials are generally amazing, his range making him very hard to approach in the air. Smash attacks are incredibly punishable, but have really good damage and knockback. Expect to use Speed and Buster a lot, as well as nair. I think he plays better defencively, racking up the damage through good spacing, but he most certainly has the tools to put serious offensive pressure on his opponent.
Overall, I think he has the tools to tackle nearly anything so he's got a lot of potential to be terrifying. If you think you'll have fun with him, you probably will.