There is great information on photo.net about this. Ken Rockwell's site can help, as can Thom Hogan's. A Digital SLR is a good place to start. Canon is the overall market leader, followed by Nikon and Sony at a distant third (Sony bought out Minolta.) Since the lenses for one system are incompatible with the others, once you choose, you will be stuck with that brand for a while. An entry level DSLR will get you started. The more you pay, the better build quality you get, the better autofocus system, the faster frame rate, and the better low light capacity. The number of megapixels is not the most important factor, although marketing often implies that. The cheapest Digital Rebel or the Nikon equivalent (5100?) is all you need.
Good lenses make a bigger difference than the camera. A good pro lens will actually cost more than the camera you buy. If you are just starting out, though, I would get the short zoom that they typically sell with it and the longer zoom. Then you will want to add a 50mm f/1.8 for $100 or so. It is the best quality to value lens in each company's line-up. The lower f/stop on a lens, the better light gathering capacity, the larger glass, and the higher price. I don't want to go through what an f/stop is here, but you should look it up and understand if you don't already.
What happens is you get going with the camera and then figure out its limitations for what you want to do with it and then add lenses accordingly. Good luck.
Oh, no point and shoot is as good as a DSLR, with the exception maybe of macro shots in a well lit environment.