Yeah, price range would be a major factor in a skeet gun. Also; do you mean trap (birds flying more 'away' from you, usually one at a time) or skeet (birds flying across your field of view, at closer range, usually two at once)? Most folks ('round here, anyway) start with trap, as the targets are moving slower. If this is the case, you can get away with an old single shot for under $100 or go up to..well, there's no limit is there? Say in the $2k range for a high quality double barrel shotgun.
For the .22, the Ruger 10/22 is a great semi-auto offered in a million variations and with tonnes of available accesories- I'm not much of a semi fan myself tho. Savage's MK II bolt-action series (the heavy barrels in particular) continue to impress me with their accuracy for a fair price. (This is at least partially due to the very-agreeable accutrigger.) CZ's 453 are another great bolt, for a few more bucks than the Savages. Just a few thoughts; there's a wide world of options to be sure.