The Audio Technica AT875 is a very nice mic for the price, and is very, very similar to the AT897. The only substantial difference is that the AT875 requires external phantom power, whereas the AT897 can supply its own phantom power via an internal battery.
And, no, the T3i WILL NOT be able to supply phantom power to any mic.
I know that you are on a severely restricted budget, but better sound requires a lot more than a "better" mic. It requires you to stop camera-mounting the mic and putting it on the end of a boom-pole, and, hopefully, getting that boom-pole into the hands of someone who has at least
some idea of how to swing a boom on a film set.
With that in mind, you may also want to consider the Rode Videomic. An RVM kit including a 7 foot boom-pole (although I would suggest at least twelve [12] feet) and wind protection is within your budget.
BTW, recording the audio to a DSLR camera is going to compromise the audio. At the very least be sure to turn off the AGC as leaving the AGC on will substantially increase your noise problems. And there will be no way to be sure that you are actually recording audio or as to the quality of the audio as there is no way to monitor the audio while it is being recorded.
You may find these threads to be of interest:
http://www.indietalk.com/showthread.php?t=49443&highlight=$1,200
http://www.indietalk.com/showthread.php?t=49544&highlight=$1,200