It's been my experience that low light shooting without a flash first requires a very thorough understanding of the exposure triangle and the tradeoffs/compromises you'll have to make shooting 'live' action in low light. Second, you'll need a 'fast' lens that can open up to f2.8 or wider (lower f-stop #s), although f4.0 is usable in some situations. Third, you'll need a camera that can handle higher ISO speeds with minimal noise...3200, 6400, etc. Just because a camera is capable of, say, ISO 12,800 doesn't mean the results have acceptable levels of noise. And lastly, you'll need a good understanding of noise reduction methods in post processing, perhaps even buying a special noise-reduction add-in program.
For a body-only, I'd be looking at a used Canon 60D or 70D, even a 7D if the price is right. A Canon 6D would do better in low light, but used prices are in the $600 & up range.