Ah! Lights.
For what you'll pay for a lighting setup, you could get some nice portraits done by a local jobbing pro. But, if you want to get into portrait work in the longer term, then buying your own lighting setup will be necessary.
You have a Fuji superzoom, which whilst it has a hotshoe, essential for triggering the lighting, is going to limit you rather. You will get quite a bit of noise on your pictures compared to a dSLR, and I'm not sure you'll be able to get the control you need for studio lighting. Anybody know of anyone doing studio work with a superzoom? Can't say I've ever heard of this kind of setup.
As well as the lights, you're probably going to need a flash meter, unless you do a lot of chimping and experimentation with the exposure.
So, by the time you've bought your lights, meter, dSLR, you're looking at a lot of money if you go down that path.
Alternatively, you could buy a reflector disc (<£20), or make your own from a big sheet of cardboard glue and tinfoil, buy a sheet of black cloth to use as a backdrop, iron a white sheet to act as another backdrop, rig up a temporary stand to hang your sheet(s) from - I found a projector screen was good for this if you could borrow on of those from someone, find a location next to a window - preferably north facing. Get stuck in and learn how to do portraits with natural light and a simple reflector.
For what you want, the studio setup is overkill.
Duncan