Guess so!
May be you should have posted this thread in the Gear section (under EF and EF-S lenses).
Here's my take on it: If you want to do sport, you need fast glass (e.g. f/2.8 ) and long focal lengths (e.g. 200mm minimum, 300mm and more!). Image stabilizer would also be nice.
You already have a 70-300mm (a Sigma). For action photography, a fast focusing lens is also very practical (and a must if you do it seriously). I'm not sure how your lens rate on this, but looking up its price, I wouldn't be surprised that the focusing speed isn't comparable with Sigma's higher end lenses (EX DG).
So here's my suggestion on it: Test your equipment, you have plenty to start off with. For action shots, boost your ISO as high as possible to give you a shutter speed as fast as possible (to freeze the motion). Yes, you will get noise, but there are softwares that help reduce this (see below). My guess is that you will always use your 70-300mm for sport shots. Once you get the hang of sport photography, you'll know what you want to get as an upgrade (either an IS lens, faster lens or higher quality optics) and your upgrade may cost you more than $1000! So save your money and spend it when you know exactly what you want!
I can give you a bit of my experience. I bought a 75-300mm f/4-5.6 IS. It has purple fringing (a sort of CA) and was taking forever to focus (trying back and forth, esp. in low light condition or with fast moving objects). I since upgraded to a 70-200mm f/2.8L IS (it costs twice your budget and doesn't have the extra range). I don't regret it. The focus is very accurate, the focusing speed is amazing and didn't notice any CA effects so far (didn't exactly look for them, but with my old lens, they were sometimes quite apparent). But when I bought my new lens, I knew exactly what I wanted.
As for softwares to remove the noise, try Noise Ninja or Noiseware (you can get free demo for both) -- I tested both and decided to purchase Noiseware, but many people prefer Noise Ninja. If you want to spend your money, these software (less than $100 ea. - and you only need one, not both!) could be a wise investment. They can be purchased as stand alone applications or as PS plugins.