$300-375 is a reasonable range for house-sharing.
I suggest you consider a house or Condo-sharing arrangement.
Search offerings at CraigsList (& teh Portland Roommate Referral Service) first, then create your Ad.
Include your usual work hours, that you are a non-smoker, & non-drug user,
and say so if you are vegetarian, a neat-nic in the kitchen, an avid recycler or composter,
if you are gone alot - & when. All that can help.
If you love to garden, or BBQ - or hope for garage or workshop space, please say so.
Are you bringing furniture?
Also include if you have pets, or are pet-friendly; or include a cat-allergy if relevant to you.
Prepare contact info for a couple of rental References in advance.
Using the Bus and Bikes is also a great bargain & an environmentally savvy,
easy way to go...I've done it for 15 years and use the savings to travel overseas.
Consider transit routes as you make your decision, at: www.tri-met.org