Which version of Maya should I download for my Windows 7 computer?
First of all, welcome to the forums!
The current version is Maya 2010. They offer a free one-month trial, after which there is a further 6 month student extension, which was way better than what I got for 09 (I had to purchase the full licensed copy to use a student, since they removed the PLE last year. 
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You can read the details HERE.
Coincidentally, I discovered this today from a colleague, and I proceeded to rant incessantly. 