Puff is an interesting match up. Normally for match up advice I'd say stay grounded in the neutral etc. But I find an aerial approach on Puff to actually be a key component in playing against her. With careful spacing and spamming of Dair, Bair, or Upair, interspersed with DJ -> Nair, and L-Canceled Nairs, Luigi can create his own 'Wall of Pain' that can compete with Puff's and prevent her from entering your space. Often, you'll even get trades. (thinking hitting a 80% puff with dair as they attempt to upair. you get free kills). Bonus points if you use platforms to ledgecancel bairs and Nairs.
Also, on the subject of the Nair. Guys. Nair kills puff at like 80-85%. If I lose a stock and I'm at a super low %, I literally throw my self at puff and let her do w/e and then Smash Di into her and immediately Nair. It's so free!
And another awesome way to combo into Nair is to Soft Nair! You can just float around the map and catch Puff with a late nair and then just DJ and kill her with a Strong one.
I find my self in the air about equal if not more than the time on the ground in the neutral vs Puff. When I'm in the air, I'm basically doing this ^.
But you always gotta keep your opponent guessing.
Alongside the aerial spamming, I play a ground game of basically pokes and grabs. Puff can crouch cancel -> rest stuff like Down-smash, Up smash and Ftilt at low % so be careful of that. But essentially zip across the stage with wavelands after spamming aerials and use dash cancelled -> Upsmashes and spaced F-Tilts. Scare her into shield and grab or jab into grab.
Luigi has great grab punishs on puff. One thing I usually try not to do is pummel, to raise chances of her missing DI on down throw. DThrow -> Chop leads to a lot of early stocks.
At lower percents I like to UpThrow into which ever aerial they Di for, usually an UpAir.
Mid % DThrow into Nair/Chop
FThrow -> WD -> Regrab
at like 60%-70%
FThrow -> WD -> Dash -> UpSmash is a favorite of mine.
So yeah.
Recovery is hard. If you're offstage you're as good as dead against Puff. Just stay on stage. Use fireballs and UpAirs to protect you're coming back. And try not to use the missile unless you ABSOLUTELY have to. Puff will just hit you out of it every time.