Nikon D50 with SB-600 that had the Gary Fong lightspheer II attached. Only thing it cost me was the cost of the blanket of snow to cover the coffee table, but most of it got cropped out anyway.
I'll also use the wall mueral we have in the kids playroom as a backdrop for portraits, though I haven't done one there in a while.
I have to do some of my youngest soon as we don't have any portrait type pics of him for the photo wall yet. I may just bring in the kids wagon and set it up in front of the mueral and go from there. Haven't tried the bed sheet idea in many years, but I may break that out too. I actually thought about doing that the other day. Trying to think of different ideas for the kids portraits. I may see if I can find an old spare tire and throw the kids in that with a sheet backgroung. Could be interesting.
There are many ideas you can do on your own. A decent camera on a tripod with a good flash and a few extra lights to fill the shadows. A room with a lot of windows can also help with extra light. I also would recommend a remote shutter release so you can concentrate more on the kids and get the timing down better.
You can also just take a picture you really like of them then change the background in photoshop or any other post processing software, to get the one color background.
Not the best editing job by any stretch. Taken with a 3.1MP Canon S30 about 3 1/2 years ago. Took 5 minutes in photoshop. Could have done better, but just to illustrate what can be done.
Have fun and use your imagination.