Among competitive shooters, a trap gun is not the same as a skeet gun. A good compromise for the occasional shooter is to get a semiautomatic sporting clays gun, and then use that for when you shoot any of the shotgun sports, including trap and skeet. I would look for a used Beretta 391. Beretta 391s were, and maybe still are, the most popular semi-auto in sporting clays circles for a long time. They are very reliable, and they came with stock shims so that slight alterations could be made to make the gun fit you better. Beretta's current version is this:
http://www.beretta.com/en-us/a400-xplor-unico/ Beretta also has a semi-auto called the A400 Xcel Multitarget. I have not seen or handled one of those as of yet, but that shotgun is able to be set up for trap, skeet and sporting clays.
Although not very popular, I have always liked the feel of Remington 1100s. Whatever you get, you need to make sure that you can change chokes. Any sporting clays shotgun you get should have interchangeable chokes.
You will want/need a shell pouch, shooting glasses and ear protection. A shooting bag is also desirable that will hold at least 6 boxes of shells and your eyes/ears (glasses, muffs). That way, when you are walking to the skeet or trap field, your shotgun will be in one hand and your bag in the other. You don't want to have to try to make multiple trips to your car for boxes of shells while shooting or try to juggle a number of loose boxes of shells when carrying your gear to the field.
Have fun!