I really recommend that people consider an SLR (single lens reflex) camera. The amount of creative control you get from having so many lens options will really improve your photography. Some of the smaller SLRs don’t really weigh that much. If you pick up last year’s model used or refurbished you won’t have to spend more than $400 which puts you really close to the price of a really nice point and shoot anyway.
Now for the question of which SLR to get. To me that is really not that important. There area a handful of brands of SLRs but Canon and Nikon are used by the overwhelming majority of pros. I am Canon user. I’ve been shooting Canon since high school. Canon and Nikon have been leapfrogging each other with innovations for decades and you really can’t go wrong either way. Both companies understand the needs of pros. Both companies have amazing lenses. There are a handful of Nikon lenses that Canon shooters wish they had access too and there are some Canon lenses Nikon users wish they had.
If you have a limited budget I recommend not spending a ton on the camera body and saving some money for the lenses. If you just stick with the kit lens that came with the camera you are really missing the best part of owning an SLR. Most SLRs come with a small zoom that is wide angle one side and slightly telephoto on the other but doesn’t have a wide aperture for low light or smooth backgrounds. You really want to pick up a 50mm f/1.8(or lower if you can afford it.) This lens will totally change the way you shoot with perfect sharp in focus areas and creamy blurred backgrounds. It also frees you from always shooting with a flash when the light gets low. All through the 70’s and 80’s the 50mm lens was the lens that came bundled with film SLRs and a lot of people took a lot of great photos with it. If I was a camera maker I would start people out with a wide aperture 50mm lens. The 50mm lens gives you pictures that are noticeably more professional looking than anything you would get from a point and shoot.
If you want to know what lens to get after you have the kit lens and a 50mm just ask me a question in the comments.