Tikka and Savage are known shooters. Remingtons are hit/miss unless you get up into the higher dollar versions, but don't forget you'll have to drop $125 on a new trigger b/c the X-Mark SUCKS!! Weatherby(Howa) are very good shooters also and come with an MOA guarantee, they just don't get as much forum time. The actions are really beefy and solid.
The big thing to keep in mind is are you going to buy the gun for $800 and shoot it stock or are you going to start upgrading parts? If you plan to upgrade, think about what model you plan to get and what upgrades you want to make. Adding a stock to each costs about the same, but doing a barrel swap can be a lot less expensive on a Savage than the others, and done at home. Savage, Weatherby's (not sure on Howa's even though essentially the same action) and Tikka all have nice triggers. As mentioned above, the Remington trigger is serviceable but no longer truly adjustable and out of box I'm not a fan. I have all 4 makes (Weatherby, not Howa) and like aspects of all of them. I think Tikka and Weatherby are the true values. Savages have jumped in price (non-Axis versions) and the recent one's I've tried, their actions feel much smoother than older versions. Remingtons have always been expensive for what you get in my opinion.
It also depends on how "accurate" you are expecting these guns to be. The cost difference between 3/4 MOA and 1/2 MOA can be thousands of dollars for the 1/4 MOA difference, and repeat-ability. If you would be happy with MOA, I think any one would suit your needs. Some of them you have better odds of getting a better shooter than expected, for the price.
Just my .02.