Your probably going to have to step a little outside of your budget zone to get a good sports lens. Some the of few lens that are sports oriented and are budget conscious are the 85 1.8 and 100 f2.0. Can you use them for football. Absolutely and they're great. The problem is for many sports they won't get you that "in your face" up close traditional sports look. If the action is in your area and you are close they will. Depends on how you plan to shoot a football game, where you are, do you move, and what you are going to do with the photos. Both of those lenses are outstanding, but for most football shooters they are too short.
Going up a little, the Canon 135L f2.0 is an outstanding anykind sports lens. One of the best anywhere. The only question you have to answer is: does it have enough reach for me. Many to most sports shooters will say it's too short to capture action away from you. Personally, I shoot all kids of sports with it. Yes, I wish I had more reach at times, but with this lens I settle for what I can get. You have to make that call.
The 200 f2.8 is very good. Nice reach, great lens, good price. I love this lens, use it often, but for me, it takes a back seat behind the 135L 2.0.
I've only given you thoughts on lens I own and use. Anyone of them is an excellent indoor/outdoor sports lens. I'd stick with a 2.8 or lower for sports (indoor and night time anyways).
The other lens that have been mentioned are excellent also. It's just that I don't have personal experience with them.
Over time, experience will tell you what lens is best for you. Have a great football season (I just finished one, playoff loss over the weekend).