I did this myself recently with an old shitty set of shells from gumtree which is why I recommended throwing the mesh heads on there. Thomann are the best bet for a set of twin ply mesh (Millenium QuiHead is what you're looking for on there). I have them set up on one kit with triggers and they work grand and also on another couple of shells I use downstairs when the kids are in bed - no issues with them at all.
For the main setup I have these as well - not cheap for practice cymbals but much cheaper than the Zildjian and Sabian low volume equivalents. Makes all the difference practice wise and they could be further damped using cymbomutes/deadbeats/etc.
Also, if you're above a living room and worried about double kick noise or whatever, you may want to look into building one of these:https://www.youtube.com/watch?v=z0Kxoa5K1vg