What's your budget? Technically, the best lens is the one you have when you press the shutter release. 45 years ago, I shot with a manual focus 50/1.4 and Tri-X for the high school yearbook from the sides and base and got more than enough decent shots. If you're talking from the stands, speed is your need and that costs, even used. Your t3 is a capable piece of equipment but you'll probably need to shoot at a high ISO. Sometimes you can get around a slower lens through anticipating action, pre-focusing on manual at a select spot, and waiting for the subject(s) to appear in your viewfinder and then shoot (IOW, no AI Servo).
Look at KEH. For example, they currently have a Canon 70-210mm F/4 Macro (BGN quality) for $74. If they had one in stock, an EX condition might set you back $91. Those are fair prices for the reach and will be a whole lot better to have a constant f4 rather than some 4.5-5.6 variable zoom. That's for HS and college games. If you're shooting Dallas or Sacramento (or even a decent pro team) and you're in the nosebleed section, 200mm will not be enough reach.