Thanks for the adice, everyone! Blender is definitly what I would end up using, since it's what I'm most familar with.
Also, the suggestion to mix-and-match avatar parts is a good one. I think the head I want is one I'll prbably have to do myself, but I've gone ahead and picked up Orange Nova's Bifrost Bunny, and I'll see if I can make a new texture+head for it.
Starting with a smallert project also sounds very reasonable! I'm not sure how the difficulty of these things scales, though- would making a clothing item be easy enough, or should I start with something static, like a piece of decor?