You can shoot skeet and turkey with the same gun, but drastically different choke requirements.For shootingskeet, you want an open choke, and for turkey hunting you will want a full or turkey choke. Therefore, if you intend to use the same gun, you will have to have multiple choke options available.
Another consideration is how often will you be shooting skeet? If it is just a couple of times a year, the Remington 870, with the Rem choke options,would work fine for you. Just screw in the skeet choke and go to the range, replace it with full or turkey choke and go huning. Also has modified and improved cylinder choke options. And this gun is very reasonably priced.
On the other hand if you want to shoot skeet much more often, I would recommend a semi-autoloader, again with the multi-choke option. The Remington 1100 is the choice here. It is a good, reliable, and reasonably priced gun. The only problem that you will encounter with the 1100 for skeet is that you will need to take a can of WD40 to the range with you to clean out the residue. As with any auto-loader, the jamming issue crops up when you least expect it, or want it. However, that can happen with a pump action as well...maintenance is the key; keep them clean.
Good luck, and let us know what you decide on.