StarChecker:
Eugene is quite do-able, we have numerous pilots and flight attendants commuting out of there. The best option is to drive. Your best bet for a base would be Portland or Medford. You could easily get either as a new-hire.
I expect you'd have to do a few months of reserve, so plan on having a crash pad until you can hold a regular line (or long-call reserve). Long-call would be a great deal for a junior guy that commutes, as you get 12 hours to report for duty. Portland traffic is a pain in the backside, so early morning OR early afternoon shows would be preferable.