First rule of interchangeable lens cameras (DSLRs or mirrorless) is to always invest in glass (lenses) and worry less about the camera bodies. Lenses last a lifetime, but cameras (especially digital ones) only last until the next model makes it obsolescent. Decide on what you're most likely to be shooting and research which manufacturer's system best fits your needs. Most manufacturers lenses only work on their own companies bodies, but there are some excellent third party lenses (Sigma, Tamron, etc.) as well that work on multiple systems.
You also have to decide on what format you'll be shooting when choosing a modern camera system. Full frame (FF) uses the same size sensor as old 35mm film cameras, but FF cameras and lenses tend to be big, heavy, and EXPENSIVE. Crop sensor are the standard at the moment for consumer cameras (like the Nikon D5300 mentioned by gert) and aren't too expensive these days. An even smaller option is micro 4/3 (m4/3) made by Olympus and Panasonic; beautifully made cameras and lenses, but not as well developed an ecosystem from companies with shakier finances. Each format has its pros and cons, so you need to weigh what you think you'll need.
That said, I can get behind gert's suggestion of the D5300. It's a slightly older model (current model: D5500) so you'll save a few dollars. I would immediately add the Nikon 35mm f/1.8 G lense. This is the basic prime (non-zoom) lens. It makes a great learning tool, and it's cheap (under USD 200). That f-number means you'll be able to do a lot of things you can't on the standard zooms found with most cameras.