I'd recommend an older second hand DLSR (you'll get a better deal and might find one that comes with additional lenses). Generally speaking a better lens on a weaker camera will give you better results than a cheap lens on a good body. Nikon vs Canon is subjective, buy what you can afford and what feels good in your hands. Don't disregard other makes such as Sony either. Knowing how to use a camera will get you better results than just buying the best and hoping it will do the work for you Any entry level DSLR with a stock lens will be good enough to get you started though.
You could also try picking up a 35mm film camera and learning the old way. You can get really good film cameras with decent prime lenses (a fixed focal range, meaning you can't zoom in/out) for a very low price nowadays. You'll need some way to develop the film though, but it's a great way to learn photography as it forces you to think about what you're shooting, how much light there is, etc.
I often take an Olympus Trip 35 out with me. Essentially it's a point and shoot, so most of the technical stuff is handled by the camera, but I can manually set the aperture to adjust the amount of light hitting the film. which lets me focus on the subject matter of what I'm shooting rather than worrying about the setting being correct. It lets me enjoy the actual act of photography and generally gives me decent results. The beauty of film photography is you never quite know how your shots will develop, it's scary and exciting at the same time.