Whether it's right partly depends upon whether you do see it as a stepping stone to something more serious later.
Chris's advice is fine, here's a bit more info to help you interpret what you research.
If you're confused by it all, by all means ask questions here at CiC.
With a brand like Panasonic, you're unlikely to go wrong, there are hundreds of P&S cams out there, granted not all in your price range, but still oodles of 'em. I expect they are all designed to be easy to use for a beginner, or they wouldn't sell.
Having reviewed the FS7 spec on the Panasonic website;
Optical Image StabilizerThese are all good things to have for what you want to do.
Intelligent ISO Control
Intelligent Scene Selector (Portrait, Scenery, Night Portrait, Night Scenery, Macro)
Digital Red Eye Correction
The biggest limitation I can see is the 4 x optical zoom I'd ignore those nasty digital zoom figures and even the "Extra optical zoom" - as both patently achieve this by limiting the technical quality of the image by throwing away pixels, so your reasonable 10MP camera soon becomes a lot less!
The zoom range; 33-132mm in 35mm equiv., is probably a good compromise, but if you did find a model with a wider range (5x or more), I'd pick one that starts at 28mm (equiv.) as it will be better for indoor shots of groups. The other reason for a bigger zoom range at the telephoto end (say to more than 200mm equiv. ideally) would be the ability to do telephoto portraits of kids (or pets) unobserved. However, this might be asking a bit much at this price, I don't know the market well.
On FS7, the exposure is Auto only, but with some overides for difficult scenes when you need them.
You will need to get a memory card for it, the internal 50MB will soon fill up (in < 10 shots). Go for a 4 or 8MB SDHC, you won't need fast or expensive (e.g. 15MB/s will be plenty).
Hope that helps, any further questions, especially if I have used jargon you don't understand, just holler,