Thanks everybody for the comments! Heres a little more technical information. In re the lighting: the light varied in each location. For Gracie (the calico) and Skye (the grey) I had natural light and a built in flash. I also have a Canon SPeedlite 430x which I used for the tortie kitten. That shoot was the most challenging for me, because there is almost no overhead or natural light in that home. My ISO on SKye and Gracie was 400; for the kitten, it is 1600.
I wonder about using a diffuser. Any thoughts on that? Or on decreasing the noise in general for low light situations?

I agree about the background being busy. I am going to photograph again this weekend, and I've requested that we use a plain light colored background only this time.

I am willing to purchase lighting, (strobe, etc) put I am not really sure what kind I need, and what would be portable. I could use some advice on that. I think it would be invaluable, since there is so much variation in light available in people's homes.

My f/stop for all pics is f4. If I pushed it to f6 would it separate the subject from the background a little more?