Should I even buy a camera at all?

Just get a low to mid level apsc dslr.  If you are shooting sports you need range so full frame isn't needed.  You need a DSLR because the focus isn't good enough on mirrorless cameras for sports.  I don't know about nikon but canon haven't uptated their sensor in a few years, so any 18 megapixel model that is a few years old like the 550d (t2i) will be fine.  The only real question is what lens to get.  The 18-55 kit lens may not have enough reach, so you might need to go for one with a longer zoom range (don't discount weight though as superzoom lenses are heavy)  This way you don't spend that much, you get to learn the ropes, and then you can decide whether you want or need something more expensive.