As the next step, and costing not much more than a good compact this camera is fantastic. Not too bulky but solidly built it fires up quickly, the 15x zoom (plus some extra digital zoom if needed) opens up a whole new experience over a compact. The focus system is usually accurate but can get a bit woolly in very low light (some form of manual override would have been the icing on the cake). Movie recording is brilliant and has consigned the camcorder to the loft forever. Some people have said the zoom control is tricky due to buttons? mine has a thumb lever that you just push one way or the other, works fine so don't know what they mean!
There is a firmware update from 1.0 to 1.1 on the Fuji site that is supposed to fix LCD display issues (I wasn't aware of any!), but easy to apply via a memory card, there are instructions on Fuji site. Check your version by holding 'Display/Back' button whilst powering up.
Other good features? flash is surprisingly powerful for its size, but not super quick to recharge, adequate would be fair.
It takes AA batteries which makes sourcing emergency power easy, with an 8gb card on full resolution its got room for 1500+ pictures so you use it a lot, best to sort out the good shots later.
I use Nimh rechargeables and as someone else mentioned the battery warning monitor is rubbish! it comes on massively too soon, even with fresh high powered nimh batteries it comes on after a few flash pictures, just IGNORE it and carry on. The camera doesn't care, recharge when your ready not when the camera says so. You will be fine.
Colour can be slightly flat in some lights so I tend to leave mine on the Fuji chroma setting rather than standard as I prefer its boost.
You can get a tiny IR remote trigger control (compatible not Fuji) if your kit doesn't include one, off well known Auction sites for a few quid works fine at 10 to 24 feet and means Dad can be in the pictures too without faffing with timers.
Can't think of anything else to add just now, but if your looking to make the step up from a compact without carrying a crate of bits and lenses around, want a good auto mode to get you started then you have found the perfect choice. Will it make you a better photographer? well your not supposed to say this but yes! It will encourage new interest in what your doing and with the zoom make you more aware of things like framing of your subject in the shot and so on, leading to more thoughtfully arranged shot. Its speed will give you new access to action shots too.