No matter what lights you end up buying, do NOT leave out reflectors. You NEED reflectors. It is pretty easy and cheap to get one of those 5-in-1 packs with the gold, black, diffuser, white, and silver screens.
Reflectors will get your subjects eyes to glow more (dual catch lights), fill in shadows, even out/balance your lighting, and in many ways, serve as an additional light source if positioned properly. Reflectors are invaluable to get the most out of your natural light outside as well.
The most inexpensive and reliable studio strobes are alienbees, I highly recommend looking into their equipment if you are constructing a studio. I currently use 3 of their B800 strobes.
Much of the point of studio strobes are control- control your light. There are many things you can use in your home to control the light- you don't have to spend money, unless you are able to. Whatever you have around the house to block and channel light, large boards, whatever, will help you direct it where you want it (off the backdrop for example).
Here are shots I did using 3 AB800s, softbox, reflector, grids, and blocks (flags). You will need to budget at the very least around $150 for decent stands for your lights, just keep that in mind (unless you plan on hanging them from strings
http://www.flickr.com/photos/frankiewit ... 396587401/
Sony A850 | Sony Battery Grip | Carl Zeiss 24-70 Vario-Sonnar T f/2.8 | Sony 70-200G f/2.8 SSM | Lensbaby Composer Pro | Sony HVL-F58AM
Alienbees B800 (x3) | Alienbees Cyber Commander | CSR+ Receivers | Grids, Softbox, Gels, Manfrotto/Century/Avenger stands