Normally, I feel like people are better off building a wheel from scratch before trying to true a wheel that's wobbly (because it's easy to ruin the wheel if you do it wrong, and even adjustment that make the wheel seem true can be a step in the wrong direction). However, in this case I think it's a great idea and something you should try regardless of whether or not you get a new bike because (a) the wheel is pretty cheap and not a great loss even if you do ruin it, and (b) the wheel isn't very old so you actually have a decent chance of saving it.

Wheel truing is a very good skill to have as a bike commuter, and you can get a spoke wrench for under $10. (If possible, go to an LBS and make sure you get the right size, probably 3.2mm.)

Check out this article by Sheldon Brown (but don't let his preliminary warnings scare you away): http://sheldonbrown.com/tooltips/truing.html




Peugeot made some really good bikes and some OK bikes. I think this is one of the OK ones. If it's in good shape at it fits (are you around 6'1"?), I would probably pay around $150 for it. I would expect that the wheels are actually 27" not 700c (unless they were replaced at some point). It will say on the side of the tire either way. If they're 27" you'll have fewer options for replacement tires. Take a magnet to see if the wheels are steel, which would make them unsuitable for use in the rain.