Err for third party lenses, all shops will ask you which mount you want, it's just the Nikon mount. The Sigma lens the TS pointed out has HSM so it will focus on his camera.
Also, just to clarify, there is no such thing as a AF-S DX mount. Nikon uses the F-mount. AF-S just means that the lens has a built in motor, DX just means 1.5x crop. For crop bodies, you don't need to make sure that the lens is a DX lens, as DX bodies can use FX lenses.
Do you have any existing lens? If you have, do you find yourself needing a lot more reach? If you do, get the 18-250, otherwise the 18-105 is better. If you don't find yourself needing more reach, then don't get anything. If you don't have any lenses yet, the 18-250 is a decent lens that can help you decide on your future lens purchase, by looking at the focal length you most commonly shoot at on that zoom lens.