Having been around when cattle were being killed, I hate that "usually" put them down part of your message.
I think Chris is right on. A good combi gun is great in its place. One of my favorites is a savage 24 in 222 over 20. To go the other way, a good 'battle rifle' like the Enfield, Springfeild, or one of the many Mausers is nearly indestructable, and shoots a very competent round.
There was a firm that was retro-fitting SMLEs for a while, and I should have snagged one when I had the chance. They informed me that they can get no more raw product from Britain.
Go to a big gun shop, and ask if they have any military bolt guns.
But like Chris said, you need to decide what you are going to need to shoot. With all due respect, I would not rely upon a 22 Hornet for a deer, unless I knew I was good enough to guarantee a head shot. I am, but once a doe moved at just the wrong time, and I shot off her jaw with a Nosler out of a .257 Roberts. There ensued a very, very long day that was more painful for her than me, but which nonetheless hurt me in body and soul.