If all you do is trap singles, a single shot will suffice. However, for trap doubles, skeet, 5-stand and sporting, a gun capable of two shots is needed.
Gun fit is paramount for success. While at the club ask folks about their guns, explain your newness - most will offer to let you try their guns out shooting them. Shouldering a gun in the store once or twice is NOT a good indicator whether the gun fits or not - shooting them at targets and being successful (or not) is. While a pump can be used, you will rarely see them on a skeet field - that extra necessary step of shucking the empty and chambering a new round tends to have most folks pulling the gun off the flight line and their cheek off the gun - resulting in misses.
A decent used semi from the likes of Beretta can be had for most folks' budgets and as it holds its value, will be easy to sell if you decide these games aren't for you.
I, personally, prefer O/U (though I do have an 1100 in 28 gauge that works well for me). I reload, and I'm tired of bending over to retrieve my hulls. I also am LH and I prefer not having empties fly across my face and field of view.
Used Beretta semis can be found in the 7-800 range around here, while a good TARGET O/U can be found for about 50-100% more. I emphasized target because many companies make similar models for field and target use, with the target versions generally being more robust and therefore heavier. In target shooting, weight is your friend. In field use weight is not.
Whatever gun you get, shoot light target loads - your shoulder will thank you. A 12 shooting 7/8oz or a 20 shooting 3/4 oz will break every skeet target and every 16 yard trap target there is. Those loads are easily realized through reloading.
Good luck!