I'm sure there is the occasional stolen phone that makes it through Amazon/eBay, but there's a lot of legit sellers as well (like myself). These sites will side with the buyer 19 times out of 20 on all disputes though, so you have a pretty good amount of protection when it comes to getting your money back.
New iPhone 5's run about $600 on Amazon, so no need to pay $650. However, you should also consider iPhone 4's (~$250) and iPhone 4s's (~$400). IMO, the iPhone 5 isn't all that different from the 4s. It's lighter and thinner and has a couple of minor improvements, but none that I think are worth the additional cost. You mentioned that you were open to used, and you should defintiely explore this path. Check out
this guide I wrote about the ins and outs of buying used cell phones on Craigslist.
Locked vs. unlocked should not really factor into your decision, as the cost to unlock an iPhone is negligible. I use
SwiftUnlocks to unlock all of the iPhones that I resell for $1.99. The only reason the unlocked phones are so marked up, is because the masses are unaware of cheap unlocking solutions, and many a website capitalize on this fact.