I've heard American brands (Chevrolet, Ford, Dodge) are notorious for starting to act quirky at 100,000 miles. Personally I love Nissan and Subaru. Honda supposedly are pretty low maintenance.
Usually you can find a good car for less than $10,000 with 30,000 miles or less which to me would be ideal. Look on autotrader.com or cars.com I'm looking at buying a Mazda Speed3 right now. One tip...don't rely on those Carfax reports for maintenance records...I bought one for my car when I was selling it...it didn't report 2 wrecks on the record that I know happened because I was driving during the wreck