I would recommend that you find the body style that "speaks to you" and then look for the nicest one you can afford. With any of these stock older pickups, you will want to do upgrades. That's what makes it yours. I believe the 3.38 rear was an option by 1962 but more likely that it would have been paired with a V8 than a 235.
One problem with that is at some point in time you may wish to sell it. Upgrading a real good factory stock truck is not a smart way to go. If you must have one upgraded look for a junker that has had that done already. Put the good one in a garage and sell it someday for the big bucks at an auction. Or yeah go ahead and mess it up with a mod then it won't be worth much. A simple gear change is okay its when you have to start cutting it up or drilling away the stockness that ruins it. Just makes tons of work for the restoration person if it ever comes to that. Sorry, its very discouraging when trying to find a truck in good shape .