I would not buy a DSLR. I would strongly recommend a cheap point and shoot with adequate manual controls and RAW support, like the PowerShot series, in combination with good postprocessing software like Adobe Lightroom. That way it's portable, you've invested very little, in case you lose interest or break it, and you still have all the tools you need to learn about basic concepts like focal length, aperture, shutter speed, ISO, focusing, and depth of field, as well as postprocessing concepts like cropping, noise reduction, exposure compensation, contrast/saturation, and black-and-white conversion. There's a saying that the best camera is the one you have with you, and that applies even more to beginners who should be taking as many shots as possible every day. Take the money you save and buy a good book or three on the art of photography, like Martin Freeman's The Photographer's Eye.
If you already have experience with P&S cameras and know all your basic concepts, a great step up into the realm of interchangeable lenses is a mirrorless camera. Many of them are comparable in price and portability to point and shoots and yet have large sensors and higher-quality lenses, offering similar overall quality to entry-level DSLRs.