Well, I'm inspired by having a sort of "generations" approach to these things (the two mini-series by John Byrne covering the Superman & Batman families across generations).
There are generations of these heroes as the older ones retire, get lost in the Phantom Zone, are killed, time travel, and so on. I chalk up the costumes as a legacy that gets passed on, but I am trying to side-step some of the questions until the issue becomes critical to the story. In fact, I've just introduced a Golden Age Superman fighting some monsters that invaded from the Phantom Zone...
There is a Superman, Thor, Batman, Captain America in this current setting, but the costumes are different and they may or may not be the same until the players interact with them. Until that time, they're free to speculate with their own preferences based on their knowledge (or lack thereof) of the comics.
My early attempts at a timeline certainly gave me a headache...