You are right about Ohio, you can only use a shotgun, muzzle loader, or handgun for deer hunting.

As to your first question, I highly suggest either the .270 Winchester or 30.06 Springfield. Either one is capable of taking all North Americal Game and your choice of ammo is th best. You can find a variety of sizes of ammo for these czalibers and since they are popular you should be able to find them anywehre (from your local Walmart to your local Sporting Goods Store).

First off, I would go out to a gun shop and see what rifle fits you the best. Get the feel of all rifles that you are considering, bring them up to your shoulder and see which one shoulders the best. You will want a rifle that fits you and is comfortable to shoot, otherwise you just invested in a large paper weight.

Secondly, go to a local gun range and see if you can shoot them there. Find some buddies into hunting and ask to shoot their rifles. Most hunters will let you try out their rifle. This is a cost friendly solution to trying them out before you buy a rifle.

Lastly, do a lot of research on the rifle that you decide to buy. Go to different gun stores, check out the internet for good buys, etc..

Good Luck!
Matt