There are a wide variety of options out there.
Two best pieces of advice...
Know the return policy. If you don't like the performance of the camera then you don't want to be stuck with it.
Learn how to use it. If you have NO knowledge of how to use a camera, even a high quality DSLR will likely not give you the results you want. So be sure to play with it extensively and if you're lacking in the knowledge area, maybe ask a friend or family member who knows a bit to help out. I've had friends on the verge of returning cameras that I knew were great until I showed them the marvels of what removing them from "auto mode" could do, heh.
For point and shoot brands, I am partial to Canon, Sony and certain Fuji models. I read a lot of good stuff about Panasonics, but I've never been able to achieve anything great with their products, but that's probably just me.
Currently I use a 3 or 4 year old Canon SD800IS. Works alright but I definitely would like something better. Problem is this one is still working just fine so I can't justify the expenditure.