Asklemmy

Sports photography is not a cheap hobby. Expect to spend 10 times your budget just to get started. You can save (some) money by shopping used on sites like adorama or B&H. Older models of DSLR can be had for a pretty good deal because all the kids these days are hyped about mirrorless. Expect to do a lot of research and wade through a lot of articles written by gear obsessed people with money to burn. I think you can still browse archives of dpreview.com for some in depth reviews and specs, especially if you're shopping older models.

Pretty much any consumer camera with an interchangeable lens will do the job, it's the lens that will really determine how good a picture you can get. There's a reason you see a lot of HUGE (and expense) lens on the sidelines. Megapixels are much less important these days because pretty much everything has enough. The metrics you'll be looking to maximize will be a fast autofocus system, a fast lens, and a long enough focal length to get your view in close to your subject from a distance. You might be able to find something that is "good enough" in a cheaper range with a camera with a built-in lens. If you get bit by the photography bug though, that might turn out to be a waste of money if you decide you want to upgrade.