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I haven't used a Panasonic Lumix but they seem to have a good reputation.
I use a Fuji FinePix 200EXR which is very compact and sturdy. I gave up the big SLR pro systems a while ago (after lugging them around America) but compact digitals do have their limitations. I'd like a Leica X1 next but they costs loadsa dosh so it'll have to wait its turn on the list.
As 'stealth' says, check out the dpreview web pages: Excellent and practical advice.
As someone else said, with things like cameras and computers, always get the most expensive you can afford.