Renting equipment is OK if you just need a piece of gear for a certain job. I've rented a few lenses in the past, but I'm pretty sure that you don't want to pay $80 every week to rent a camera that you're just learning to use.
And $1200 is pretty steep for a T3i. I got my 7D with a 28-135 for $1400.
Edit: Sports on a budget? Get a used 70-300 for a couple hundred bucks and you'll get a good feel for what you need should you decide to upgrade.