Don't believe your father's old-fashioned warnings about buying used. Buying a "pre-owned car" means you've let someone else drive those expensive early miles.
Do your research, of course, and look for a reliable model. But today's cars can generally be expected to rack up six-digit odometer numbers before experiencing major mechanical breakdowns.
Check ConsumerReports.com for detailed reliability information. Sites like Edmunds.com and Kelley Blue Book's KBB.com can help you narrow down the price you should pay.