Stages can be very complicated choices for Luigi, and I've been known to go back and forth with my opinions on them.
DL64 - Great stage for Luigi all around, but it certainly can be used against him. Characters with better recovery like Peach and Samus will definitely give you a hard time here, but you can make it work. Fast characters can be dealt with but you might not want to take them here if they like to camp.
FD - Yes you can destroy fast fallers here (side note: versus Falco you should really learn to powershield or you might hate life). Some characters like Falcon and Ganon have a hard time approaching and escaping juggles without a platform. The same can be said for Luigi versus Marth or Sheik. Fighting Peach, Puff, and Samus here is something I've gone back and forth on. On one hand each character has something that platforms help you deal with (floating, bair spacing/aerial mobility, and projectile camping respectively). As Luigi players we want to use our awesome aerials and platform movement and we forget that Luigi is by far more dominant on the ground. Choosing FD will help you play with much more discipline, which may be the edge you need in the matchup.
BF - Pretty neutral for Luigi, this is probably your best choice when you don't feel comfortable going anywhere else. Everybody is going to be practiced on this stage but you can do just as much work. The lip hinders Luigi as much as it hinders anyone else, so don't worry too much about.
YS - Luigi has very powerful combo and stage control games here, as well as aided recovery with the wall and Randall (learn your Randall timings!!). This is a big personal preference stage, if you feel comfortable that you can get control and keep it, take them here, if not, avoid it. Characters like Marth Ganon are very powerful here, so definitely avoid them.
FoD - This is your counterpick if you're maybe hoping to cheese your opponent out, and that can go for pretty much any character in any matchup. Luigi has the tools to use Fountain to his advantage, but you have to put in the effort to know how to abuse Fountain better than your opponent. I CPed a Falcon here once because I thought it might be free but he ended up destroying me with stomps through the platforms. Again, use at your own risk.
PS - Nice open space for Luigi with platforms to work with to boot. It's low ceilings open up early SJP kills as well as up smash and nair. The camera makes you slightly harder to edgeguard if you can use your tornado and double jump stalling effectively. Grass transformation is good for Luigi, water is okay. Fire can be dealt with if you simply resolve never to cross over the tree and you can avoid being wall comboed. Rock is very dangerous from any part of the stage. Luigi can win in the pits and kill from the top of the mountain and get silly with the weird edge but these are all dangerous situations that can quickly get you killed. Try this stage out in multiple matchups to see how you feel in each.