I hunt deer with a Sigarms SHR-970 (Swiss Hunting Rifle) in 30-06. I paid $450 for it new in 1999. The only "action" smoother than the Sig, was an $800 Weatherby. Even then, it wasn't "that much better".
http://www.sigsauer.com/upFiles/CmsContent/documents/OwnerManual/SHR970OM.pdf
I'd go either .308 or 30-06. Ammo is more openly available, 7mm Mag is getting tougher.
I love Sigarms SHRs!
All that I've ever used end up there on my list of "best bolt-action rifles".
I've had the pleasure of trying a variety of cartridges in SHRs (.22lr up to .30-06). My favorite one I've shot was a friends 30-06, I must of put 600 rounds through it one afternoon just shooting at cans. Their compfort, accuracy and smoothness of the action is just... a piece of art (another feature I really like about SHRs because I mostly target shoot and can go through a lot of ammo on a good day: of all the bolt-actions I've shot they have my favorite removable magazine - solid and well-machined yet still slim and light enough that you'll forget you have one in your pocket). Ever since I've had wet dreams about getting my hands on a Sigarms 30-06 of my own some day.
Mash, you really should find a friend who owns one and grab a couple cases of ammo. Compared to the rest of the rifles in your collection, I'd like to know what you think about about one.