I live in NY... Shotgun only here for deer.
Ideal starter setup: Remington 870 express. I'd go with a 12 gauge, but that's my preference. The kick shouldn't be of any concern. If it hurts, you're holding the gun wrong.
The price is good and it comes with 2 barrels. One for slugs (deer and bears) and the other for shot (just about anything else)
Pick up a 5 pack of 3 or 4 different brands of slugs... see which one shoots the most consistently (site on the same point, shoot 5 times - find which brand has the tightest group) Then adjust the sites so the group is at the center, and use that brand.
Do the small game thing before deer season... you'll grow more accustomed to the gun, plus it'll seem a lot easier and lighter to use once you switch to the deer barrel. (Something I recognize a lot now, since I switched to a 22 for small game - something I regretted last year when it became difficult to get the sites on the kill zone quickly) Scope is unneccesary, but some people I know like over-under scopes (or whatever they're called) so they can use either the open sites or the scope, depending on the situation. The scopes are pretty cheap for the power you'd need, and if the deer is standing still, a "perfect" shot at 50 yards may be more preferable than being 8 or 10 inches off. I don't use a scope but have been considering one for a few years now.
Wallyworld sells them for under $300. A majority of the hunters I know started with similar setups for equipment and after a couple of years have switched to $600 and up guns, with a minimal increase in affectiveness.