It would be impossible to accurately put together a list of combos for Luigi. His movement coupled with his moveset allows him to put together some creative combos. You just need to know some basics:
- Utilt/Dsmash/Usmash/Nair all pop people up and can lead to more utilts/nairs/dsmash/usmash/aerials. You can link a number of these moves together, for example chaining multiple utilts together.
- You can perform two aerials in a short hop which allows a fair amount of mix up potential. You can pressure people's shield by doing dair -> nair in a single short hop. If they try to react OOS after the dair, then the nair will pop them up and set up for a combo. This is something that a lot of Luigi's do however, and your opponent will catch on and try to bait you into doing it and punish you for it. As a result you can mix it up by only doing the dair and then landing and trying to grab/smash their reaction, or do something completely different!
- Luigi's Uthrow/dthrow both set up combos. Dthrow -> dsmash works on FFers/mid weights at low/mid % and leads to fat combos. I know Abate will jank people by WDing backwards into his opponent, grabbing them and immediately dthrow -> dsmashing before they can react and DI. This setups FAT combos.
- Luigi's aerials are typically the finishers in your combo, and they are pretty good. Fair/Dair are both strong, and even bair/nair can KO. Uair is an underrated juggling move, but his other's that I listed are better.
Hope that helps! Practice makes perfect.