Novelle, in general the last place you want your flash unit is at the camera. The reason is that it produces no modeling. It is just flat, in your face, headlights-on-the-deer-in-the-road kind of lighting. So if you buy a larger flash gun and put it on the hot shoe you will get exactly the same lighting but with more available power.
The idea is to get an extension cord for the flash so that you can hold it away from the camera whether you bounce the light from something to soften the light or not. So until you're ready to take that on, I wouldn't recommend getting another flash unit. If you are, then there you go.
To help with the fill question, fill is whatever adds light to shadow areas in the subject. If you have illumination coming to the subject at an angle, you can "fill" shadows partially or completey by adding a second light source (it could be just a reflector, as an example) at whatever angle works to reduce the darkness of the shadows.
I always recommend that beginners start by using window light and a reflector. I recommend getting a large piece of white foam core to act as the reflector. Then fool around with different subjects, different times of day, different distances and angles for the reflector etc. That will give you some additional experience at how light behaves. What we are normally trying to do with artificial light is to produce something that looks like natural light.
When you move to flash light, everything is really the same except for the methodology for generating the light. I had a tendency to use a lot of reflectors in the studio mostly because I learned how to light subjects at a window.
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