As others have pointed out, that's a VERY tight budget. If you're really comfortable spending close to the upper end of your budget, here's what I would suggest for right now. Pick up a used 40D body and a used 85 f/1.8. That should run you somewhere in the $800 - $850 neighborhood, depending on the deal you get. That should do you pretty well for basketball. Just realize that you'll pretty much be shooting at one end of the floor. Save some money for baseball season and pick up a used 70-200 f/4 (or f/2.8 if you get a nice tax check!). A used f/4 version will run ~$500 and a used f/2.8 version will run $900-$1000. You can add a Kenko DG300 1.4x TC for ~$100. I shot a year of rec. league middle school lacrosse w/ a 40D, 70-200 f/4L non-IS, and a Kenko 1.4x TC, and was VERY happy w/ the results. Here's the key thing to that though. All the games were played on the weekends, during the day, so most of the time, there was plenty of light.
When I moved to shooting HS lacrosse, most of the games were after school, starting at 4:00. Not really a problem for the Varsity games, but the JV games started closer to 6:00, and in the Spring, you really start to lose light at that point in the day. Sold the 70-200 f/4 and bought the f/2.8 non-IS version. Also picked up a Canon 2xTC II. The 40D + 70-200 f/2.8 + 2x TC worked great when there was still plenty of light, and I would just pull the 2X and go for the 1.4x as the light faded. If the games ran long, I would just pull the TC off all together. I would adjust my shooting location to focus on one end of the field, and everything was fine.
7D, BG-E7, BGE2x2 (both FS), 17-55 f/2.8 IS, 17-85 f/4-5.6 IS (FS), 50 f/1.8, 85 f/1.8, 70-200 f/2.8L IS Mk I, 70-300 f/4-5.6L, 550EX, Kenko Pro300 1.4xTC