What to Look for In a Fixer Upper
Check for something that has easily available parts.  If you buy a bike that's too old, then new parts won't fit on it properly, and you'll have to either find old parts in good condition, or pay more for parts because they aren't made in high volume anymore.  I guess if you're talking about a commuter, then it's going to be a road bike. Make sure that it has 700c wheels, or can accomodate them.  Otherwise, finding 27 inch wheels and tires can be a bit of a pain.