As a beginner photographer with no lens collection, you'll likely get by initially with any DSLR body, with the lens being the more important choice off the bat. If you wanted to get into 'serious' sports photography, like career-wise, that's a different ball game, if you'll excuse the pun. But assuming you mean casual/amateur shots of sports, even a more entry level camera body paired with a decently fast telephoto lens should get you good results. but likely you'll want to be hunting for more than 135mm, and likely want something much faster than basic kit lenses.
It's up to you if you want to limit your choices to only two brands - obviously less models you have to look at and consider, and makes it harder to determine if you are getting the right and perfect camera for you (let's say you pick the best choice between two brands, but a 3rd or 4th brand's offerings actually would have fit you better, had specific features you wanted, or could have made you more comfortable or capable...you'll never know, since you never considered them). In the end, you could look at all brands and find that a Canon or Nikon model is the best choice for you after all, but at least you can be confident in that because you did look at all available options. I really would recommend you consider what Sony, Pentax, and Olympus have to offer, just so you know the field and any special features those models may have advantage over Nikon or Canon FOR YOU. You can't really go wrong picking from any of the big 5 brands - and all have a fairly decent lens selection, used and new (even the least of them has some 100 or so used or new lenses available for the mount, far less than Canon or Nikon, but likely far more than you'll ever buy in 3 lifetimes!).
BTW - lack of FPS can have an impact, but it won't make or break a good photo - it just improves your chances of getting a good photo. If during a play, you fire off 4 frames, you may get the perfect pose and moment in one of those 4, or you may have just missed it in each frame because of closed eyes, something blocking a face, a little extra motion blur, etc. If in that same time, you were able to fire off 10 frames, you have a much greater chance of having caught the precise perfect moment...no guarantees, but more frames of the same action can increase your hit rate. There are several cameras in your price target capable of 4.7, 5, 7, even 10 frames per second...they'd be worth considering at the very least.
Sony DSLR-A580 / Sony 18-250mm / Minolta 50mm F1.7 / Sigma 30mm F1.4 / Tamron 10-24mm / Tamron 150-600mm / Tamron 90mm F2.8 macro / Minolta 300mm F4 APO
Sony A6000 / 18-55mm F3.5-5.6 / 55-210mm F4-6.3 / 10-18mm F4 / 35mm F1.8 / 16mm F2.8 / via manual adapter, lots of Pentax K mount, Konica K/AR mount, and Leica M mount manual lenses