Welcome to the forum.
I'm sure that it's a pretty good camera, for what it is. The Finepix line of cameras are quite popular.
For some people, it may be good enough for action shots and low light shots...for some people...it might be very inadequate. Will it be good enough for you?
I don't like that type of camera (what I call point & shoot Digicams) for action shots because it typically takes a while to 'snap' the shot after the button is pressed. It may only be half a second, but that's enough to miss the action shot...or miss a facial expression.
Also, those types of cameras may have a few ISO settings but the higher settings produce images that are full of digital noise. (although they are getting better all the time)
The type of digital camera that I have (and many people here) is a digital SLR camera. The main advantage is that the digital sensor is much bigger than the ones found in digicams. This along with better electronics, allows a DSLR to use higher ISO settings with lower noise...which is a big help with low light shots. Also, they have an actual shutter, like a film camera...so they are much quicker to snap the shot when we press the button. Another advantage is that they allow the photographer to change the lens. You can put on a lens that will suit your purpose...wether that's landscape, sports, portraits or whatever.
The trade off is money...DSLRs are expensive but getting cheaper all the time. Also, the lenses are expensive...and the really good ones are very, very expensive...but they hold their value better than any digital camera because they mostly interchangeable with newer cameras.
If you are serious about photography and want to get shots that a typical digicam just wont get...I'd suggest an entry level DSLR. Something like a Canon Rebel XT or a Nikon D50. They may be more expensive than the Fuji you are looking at...but they are much, much more of a camera.