Your First DSLR Camera
Digital Single Lens Reflex, or DSLR cameras are great. Today DSLR's have more features, work harder and work smarter so you can do the creative and allow the camera to do the technical! Today's camera's also allow you to control the technical aspects and to learn faster and cheaper than traditional film camera's did. Remember, Digital means no more spending $10 for each roll of film, plus an additional $10 to develop what most rolls were: bad photos! Going digital means making more images, more mistakes and learning.
If you want to get into DSLR, but you're not looking to spend a lot, both Canon and Nikon make low end models. The camera body allows you to start getting used to features, master the ability to control the image and light by mastering aperture and shutter speed, etc, and then to start experimenting with lenses.
When you buy the low end model Nikon (I know Nikon, but I'm sure Canon shooters can jump in with similar models from Canon) like the D3200, you get your first lens. Often, the kit lens gets a bad rap. But remember, the camera, and lens is far and away above the tech and gear that we had on the market a dozen years ago. Some amazing photographers learned to make fantastic images on some of the 'bad gear' of the time.
It's really all about mastering light. Your tools: Aperture, Shutter Speed, ISO. Learn to frame the subject, etc. It's not the gear, it's the photographer. After all, you don't go into a fancy restaurant and ask the chef, 'What kind of pots and stove he uses,' do you?
BTW, if you take a look, Nikon, Canon, Olympus, and Sony all make cameras classified as 'Mirrorless.' They have some of the features of Point and Shoot, like ease of use. And some features of the DSLR, like interchangeable lenses. Unfortunately, the lenses you buy for a Mirrorless are not compatible with a DSLR. I think the price for the Nikon N1 Mirrorless is about the same as the price of the D3200, so not sure you really save much.
Another option is to go to a local camera store and buy an experiencedcamera (we call them used!) You'll get a decent camera, and $ave money. Used cameras are usually a good deal, as long as you can take it back within a reasonable time. This should give you a week to shoot, and download and see if there are any major issues.
Just Do It!
What's really important is that if you have the passion, don't spend obscene amounts of money on the fanciest piece of gear you can. Get your first camera, and start to understand How To Take Photographs.