You're going to love Portland. Best city on the planet as far as I'm concerned. Coincidentally, I'm here for school also--law school at Lewis & Clark. Where are you going to school?

A cyclocross bike with a triple would be fine for the fire roads out here. You could also get along fine with a touring frame that would allow room for 700x38 or higher tires. Lots of touring frames are designed to accept large tires with clearance for fenders, so whether you're on a cyclocross frame or a touring frame you'll likely end up running similar tires. Cyclocross frames often lack braze-ons for fenders and racks, though. Don't underestimate the necessity of fenders in Portland, so make sure it'll be relatively easy to mount fenders and racks on whatever you buy. Other than that, it really comes down to preference on what kind of riding geometry you like, fit, price, options, etc.