There are a lot of options here. First I want to talk about soundproofing. Insulation helps with absorption, not soundproofing. Soundproofing requires mass (like extra sheets of drywall, deadsheets, etc.). If the others in your house don't mind hearing drums, then the real issue is how much nosie will get in to your studio from the other parts of the house. Is there a lot of footfall noise (can you hear people walking on the floor above you)? If so, this can make your situation tricky. Assuming that your isolation is adequate, for equipment you need something to record to. Do you want to record to a computer? Then you need a nice computer, at least a dual core machine to run the majority of programs and effects. You also need a program. If you intend to work in the professional community, pro tools has become kind of the de facto standard. If you are going to be doing your own thing, there are a ton of other programs around. Cubase, Sonar, Logic (if you use a mac), DP (also for macs), and the list goes on. It depends on how much you want to spend on a computer program, because good ones can range from like 50 bucks for reaper to hundreds (thousands for a pro tools tdm system). If you go with pro tools, you have to buy their interface and plugins can be more expensive for it than for other programs. If you go with some other program, you can choose your own interface. Motu makes great firewire interfaces that you can daisy chain to record up to 32 tracks simultaneously (I think it's 32, not sure). There are a ton of interfaces out there besides Motu that would work also. Trying to create an equipment list from scratch is like trying to paint a painting from scratch with someone saying "paint something pretty", most everyone will come up with a different end result. What kind of music will you be recording? How many simultaneous tracks? Will you be working with midi much? How much post processing do you want to do (plugins, etc.)? There are a lot of things to take into account here.
