Rent depends a lot on where you'll be living. I rented downtown for two years while I was in grad school and I paid $800/mo for a 400 sq ft studio apartment (six years ago). Obviously the farther you get from downtown, the more rent goes down.
My second apartment was about half the cost, BUT, you had to be a student (of any school - Portland has many: art, culinary, liberal arts). I can't remember if it was required to be a full time student, but if you're taking classes, it can cut your costs a LOT. However, the atmosphere is very much like a dorm - frequent fire alarms & late night noise.
There is also low-income housing. You might actually qualify for that, but I'm not sure if they check on investments. Again, there is the atmosphere to consider. A lot of these brand new buildings get super run down in a very short amount of time.
All that to say, if you want a nice place, I'd plan on budgeting $800/mo or getting a roommate.