Sounds like an exciting endeavor! You can get into a small studio setup fairly inexpensively. In fact, if you spend right you can be setup decently for under a grand.
Camera: The top name brands Canon, Nikon, Pentax, etc. have SLR models that start around $500. You can get a Nikon D40 or a Canon 40D in this price range. Go look at a shop, or you can buy online at adorama.com or B&H (both popular suppliers with photographers) Try this link:
http://www.adorama.com/Catalog.tpl?
page=il_refine_search
Any of these would work well for your application.
Lighting: You can get into a small 150w 3-strobe (3 lights plus accessories) setup for under $200. Keep in mind, however, these have a learning curve so if you go this route you might find yourself experimenting a bit. You might consider purchasing a camera mounted flash. I'm not familiar with other brands, but I use Nikon SB-800 and SB-600 flash units. Flash units like these are great because they work in conjunction with your camera to determine the right exposure.
Backdrops: Like any other gear, you can wind up spending thousands on stands etc. Most backdrops you purchase are of muslin material, which you can purchase at any local fabric shop. It's used typically for bed sheets, and is available in different widths up to around 10 feet or so. It's mostly available in white and can be dyed and painted. You can come up with a way to hang and/or drape your background or you can purchase a background stand for about $100 which work well.
So, contrary to what you may hear, you can be up and running in an afternoon and for under a grand. Pick up a fashon magazine on your way back to the studio to get a few ideas for poses and start shooting.
If I were going (and this is just my opinion) to do this, say today and on a tight budget, this is what I'd be looking at:
Nikon D40 with kit lens $500
Nikon SB-600 Flash $200
White muslin 10'x15' $50
Background stand $100
Don't forget to post some photos and let us know how you're doing!