A couple thoughts for you.
1. With whitetail, varmints and pigs in the mix, I'm thinking you will likely want to be able to put a scope on it for varmints. From a collecting aspect, most of the models were not factory drilled and tapped for a scope until the 1950s, and 99s drilled and tapped after they left the factory are no longer original, and not as collectible. There is a special scope mount available made by a fellow in CA called a Lightfoot mount that uses the rear tang taps and the rear sight dovetail that can be used to put a scope on an original, non-D&T'd 1899 or 99.
2. Do you reload? If not, as much as I like the 300 Savage, commercial 300 Savage ammo is limited to 150 and 180 grain ammo. Not sure you would be ok with that for varmint hunting (if you are ok, then 300 Savage would be on top of my list). A 99 in .308 would offer many variations of commercial ammo.
3. Do you shoot left handed? If you do , the 99s moved to a top-tang safety in 1960 that would be better for a lefty than the lever-safety version on the 99s made prior to 1960.
4. If it were me, I'd look for a .300 Savage made in the 50s that is drilled and tapped for a scope; I can reload various bullets. If I did not reload, and needed bullet selection for deer, pigs, and varmints, I'd look for a 308. You would be looking for a Model 99EG, 99F or a 99R (pics in order below).The 99R is bit heavier, but seems to be one of the most accurate 99 models. The 99F is a featherweight, and one of my favorite models for hunting with a 22" barrel (the EG and R are 24"). A 99EG in 300 Savage would be easy to find ... there are lots of them out there. If you went the .308 route, I'd be looking for 99F.
The 99s made from 1960 on are not as collectable, but they are still nice rifles, and there a couple more models (a baseline model 99E, a saddle gun model 99A, 99F, 99DL, 99C and 99CD (the last two have detachable magazines).
Some models were even offered in .358 Win, .284 Win and 7mm-08, but they are very collectable, hard to find, and pricey when you do find them.