Hi Nick and welcome to the forum,
I've had a play with a TZ10 recently and for a compact superzoom camera it is very impressive. The Aperture mode does allow you to use more than two settings you'll be pleased to hear, but as a general rule this mode would be used on a DSLR to control the depth of field and on a compact it is almost impossible to get a blurred background when your shooting something in the foreground. Owing to the small size of the sensor it tends to keep everything in sharp focus.
The Shutter Priority mode though, works very well and of course, if you're one of those people who when they get home and have their photos printed and cannot remember where they took some of them it has a built in GPS positioner to help you find the exact spot. If you don't need this facility, then take a look at the TZ8 instead. Virtually an identical camera, except for this feature.
As Chris mentioned, a hybrid bridge camera is often the best option if you're wanting to learn the basics of photography, because they come with more DSLR like controls, but you're not making such a big investment as you would in buying a DSLR and all the kit that you need with it, so if you find photography isn't really your bag then your outlay has been much smaller. The cameras Chris mentioned are all very highly regarded, though the SX20 and FZ45 receive the best reviews overall.