A big part of how good your pictures turn out depend on how much you know about taking pictures. I mean, you can have the best camera in the world, but if you don't know how to use it properly you are going to get crappy results and your investment will have been a total waste of money.
Now that I've gotten that out of the way, I would suggest at least a 5 Megapixal camera or better.
There are a number of good quality digital cameras that offer a wide variety of automatic shooting modes with some wide angle to telephoto zoom capability built in. Some of them even have a macro setting for close up photography.
However, if you really want flexablity and a camera that will grow as you learn, then I would suggest a digital SLR. I would stick with the major brands like Canon, Nikon, and ect., as they have been around for a very long time and they are top quality.
Personally, I prefer Canon cameras and printers. I bought my first Canon 35mm SLR back in the 70's and took thousands of pictures with it. Then, a little over a year or so later, I traded it in a bought a much better model and a second body, and took several thousand pictures with the two cameras over the years.
I finally retired those cameras and bought a newer model around 6 years ago, I think.
Now, I have my eye on the Canon digital SLR (the new Digital Rebel XTi or the Digital Rebel XT). Either one would do just fine for me, and they would work with the lenses and flash that I already have for my 35mm camera.