That's a great camera, and a pretty good lens. But night sports is a tough environment and really calls for big, expensive glass.
I shoot a lot of night sports with a 7D and generally go with: 1/200 second, ISO 1600, and from a monopod. I also use a 540 EXII speedlight when I can (highschool) games. turn to M on the flash, 1/128 power.
Your f5.6 lens is your biggest problem with night games. I have a 70-200 f2.8 IS II, which is awsome, but way exspensive. A friend shoots with the 70-200 f4 IS and while good, the 2.8 is much better. I turn my IS to mode II, and pan as much as I can.
The 60D is a great camera, and with that lens you'll do much better in the day. I'd invest in lenses if/when you can. And borrow if you can. Consider a Sigma, or used vesion 1 of the Canon lens. IS is nice, but not critical. Use a monopod. Even a decade old Sigma 70-210 f2.8 (maybe 4-500 on eBay) would be good budjet choice.