I am looking to setup a portable studio, one that I can setup in houses I go to take pictures of people, like families and stuff.
I do this fairly often.
For my background, I have a Dynatran background support system (from Amvona.com) $100. I don't have muslin backdrops yet, so I use bed sheets.
For lights, I have three studio strobes from
www.Alienbees.com and I'm thinking of adding a fourth. Lights with accesories (softbox, umbrella, stands, honeycomb grids etc) is about $1000.
I trigger the lights wirelessly with a cheap radio transmitter from E-bay ($40)
Light Meter.
Then of course, there is the cameras & lenses etc.
I wouldn't call it the most affordable set up, but I think it's much better than struggling with inferior equipment.
You could try to using continuous lighting (incandescent, halogen, fluorescent) rather than strobes...but there are some problems with that. Firstly, you would need a lot of lighting power in order to fast shutter speeds...which you will want, because slower shutter speeds make for blurry photos when shooting people, especially kids. With strobes, that is not an issue.
You could also try using cheaper strobes, but the cheap ones may be under powered for shooting more than one person and it will limit your options and creativity.
Another option would be to use hot shoe flashes, like what Patrice is describing. Although, high powered flash units are not any cheaper than my studio strobes.