The biggest thing to do is to check in early. Southwest has online check in, so take advantage of it.
Airlines will almost always go by time of check in if the flight is oversold. They can indeed though check to see what "fare class" or how much you paid for the ticket, however they will rarely use this to bump people unless the bottom of the list is a frequent flier/full fare person that they would have to bump otherwise.
If you are wanting to get bumped (some people have the time and use the credits for their next trip) pick flights that are almost sold out or are sure to sell out (holiday weekends etc.) Check in as close as possible to the cut off, however do not be late (they can cancel with no compensation if you miss the cut off). When you check in, ask if the flight is oversold and volunteer to be bumped at that point. Also when you get to the gate, tell the gate agent that you volunteer to be bumped if they need to. Volunteering will put you ahead of those who check in later.