I don't often need three lights for pets; sometimes, when I want to shoot a white dog on white paper, I'll blow the background with a third light. Otherwise, two will do.
Also, I tried cloth backdrops; I like them, but they have a HUGE disadvantage: a pet WILL soil them, and they are then unusable until washed. (Yeah, you CAN use them, but the next client sniffs that darned spot and won't pose!!)
Start out cheap; get on eBay and buy a wireless flash trigger for $35 ... well worth the money, and you won't have to worry about someone tripping over your wires!