Well easily the most important thing to know is how his side special works. It initially appears weak, but it actually grows in power the more times you land his up and neutral specials. Once his side special is at max power, Wright will glow and his taunt will change to indicate this. Getting KO'd will make you lose all progress toward increasing your side special's strength, however, so be careful. His down special works like Villager's pocket - catch a projectile and throw it back. I tend to suck at catching projectiles though, so I'm not positive about the details concerning that one.
So, tl;dr, use Hold It! and Objection! a bunch of times, then use Take That!
Wright's normals are pretty weak and his strongest ones tend to have crappy range (and some of his bad ones have crappy range too), so you'll want to play defensively and rack up damage with his papers and such before trying to score a kill. His best and probably only kill move outside of a powered-up Take That is definitely his up-smash, if you can manage to land it. His f-smash is slow and does horrible knockback, but it does really good damage if all the papers hit. Think of it more like a projectile than a smash attack. Can take some getting used to.
EDIT: Forgot to mention, his b-air has pretty good knockback, and is capable of killing unsuspecting foes at high percentages. Down aerial is quick and has a great hitbox, and I'd say it's his go-to aerial attack, but remember - if Wright hits the ground during it, he'll pratfall, so remember to tech when you use it. His other aerials are alright too, though personally I tend to avoid his neutral aerial most of the time. For a sex kick, it's got a pretty odd hitbox and pretty terrible range.
As for whether Wright has any meteor attacks, to my knowledge he only has one, and it's unexpected - his down throw. That thing will throw you straight downwards if he uses it near a ledge...though positioning yourself correctly may be tough. Otherwise, most of Wright's moves will generally send you flying upward (even his jab, for some reason lol).
In my personal opinion, Wright isn't very good as it stands right now - Take That is somewhat laggy, he loses all progress toward buffing it if he dies, he lacks other good KO options, his projectiles don't travel very far and he only has one fast one that sends you up, so it's not the best tool for long-range spacing, his down-special is rather situational, and his moves don't really have low enough knockback or endlag for a lot of combo potential. I'm sure future updates will address these issues. On the plus side, he's pretty hard to approach because his jab is REALLY good at walling you and, regardless of my skill with it, he CAN stop energy projectiles with his down special easily.