We all pretty much came up through the equipment struggles. Noise is always more apparent when the shot is underexposed and brightened in PP. As was mentioned above, the flash is the most cost efficient solution in the short term and I agree with Brent that manual flash is the way to go. Nikon CLS is really good in some circumstances, but does not give consistent results especially for sports. Good glass is the best route for the biggest inprovement but also more costly.

I have seen the 80-200 f2.8 model that I use online in demo condition for under $800. The thing is a tank and it is a reference model for image quality. Keep shooting and working on the gear you want, you're looking good so far!