I only skimmed the first page, so forgive me if I cover something that has been said.
Areas that allow rifles have a minimum caliber restriction. In Texas, rimfires are illegal for big game. Rifles are illegal for turkey in the spring, etc. In Colorado, the restriction is based on the amimal. Larger calibers for larger animals.
In New York, some wildlife management units are closed, some are bow only, some are shotgun and muzzleloader and handgun and bow, and some are rifle and shotgun and muzzleloader and handgun and bow. The restrictions apply whether the hunter is on private or public land and are carved in stone, so to speak. Refert to the following page for details about what arms are legal in the area you plan to hunt:
http://www.dec.state.ny.us/website/dfwmr/wildlife/guide/legalimp.html
Additionally, it is
ILLEGAL to hunt deer with
any rimfire rifle, a fully automatic firearm, an
autoloading firearm that holds more than 6 shells (except an autoloading pistol with a barrel length under 8 inches);
any firearm equipped with a silencer...
Leave the SKS and the .22 at home.
I would recommend a remington 700 in anything from .25-06 up to .300 RUM. I shoot a .270 and my wife shoots a 7mm remington magnum. A .270 will take anything up to and including an elk, and serve you well as a varmint gun as well. A 300, any of the long action 300s, is good on anything that north america has to hunt. A 338 is excessive for whitetails.
My personal recommendation on caliber would be to pick the largest caliber that you can shoot comfortably, and practice excessively. A large and fast, but poorly placed bullet is less effective than a small bullet placed well. There is no better way to develop a flinch (the death nail to accuracy) than shooting a gun whose recoil you don't tollerate well.
Additionally, look at what you are going to be hunting, or what you may want to hunt in the future. If all that you ever want to hunt is white tails, then a 25-06 would be killer. If elk are in your future, then maybe a 7mm or 300 would be better. Remember that a .270 will do a number on an elk too. Shot placement and terminal ballistics (how well the bullets stands up to the game) are more important than caliber, but caliber is important too. A 300 in the gut is less effective than a 25-06 in the heart. A 70 grain frangible bullet will be less effective than a 180 grain bonded core/A-frame/partitioned bullet. If any or all of this sounds confusing, then you have some homework to do. E-mail me and I'll try to make it make sense.
