In the camping section at WalMart they have inexpensive rain covers for backpacks. They are probably not the best quality, but may be adequate for your needs. Another option would be to fashion a cover out of an inexpensive rain poncho and some Gorilla Tape. Perhaps a heavier plastic bag would be more durable and reusable that a trash can liner.

I too am wondering just what kind of touring you will be doing on a budget so tight. I'm all for self-sufficient, minimalist, living off the land type of travel, but you need to have some kind of budget for supplies, repairs, emergencies, etc.