Before you buy, handle them all. You'll have the most confidence in the rifle that "feels" right for you.
As stated before, $800 will get you a very nice mid-range rifle. My choice, hands down would be the M70.
That said, I have a Tikka T-3, a CZ 527, and just bought a Ruger gunsite scout and they are all great rifles also. Just the M70, IMO, is the best of all of them in terms of quality.
The Tikka is my least favorite because of the cheesy magazine, no controlled round feed, stock is flimsy, and it is difficult to load single cartridges in through the ejection port. That said, it definitely performs better in terms of smoothness and handling, outstanding trigger, and the best accuracy by far I have ever had from a stock rifle even with factory ammo.
I have no experience with the Savage, Marlin, and Remington rifles and don't care too. But many people swear by them and I would not over look them. Once again, handle them all before you buy.
For top shelf stuff you will have to spend much more.
I had a custom M70 built with all of the bells and whistles for $3,800 and it is a 1/2" rifle, but if I had it to do over again, I just would have stayed with a stock M70. The dream of owning the perfect rifle built to your specs is nice, but in the field it does not pay off in terms of value for your dollar. It pays off in terms of the satisfaction of owning a custom rifle and there is a dear price to pay for that. Now that I have been there, seen it, done it, I won't do it again.