For me it is a toss-up between the Remington 700 and the late Winchester Model 70 for #1. Quality seems equal and accuracy seems equal.
While Remington is often cited for accuracy, the 4 Winchester Model 70s I have owned have been extremely accurate. I recently traded a sub-MOA 70 Ranger .270 for a 70 XTR .25-06 but haven't played with that yet to see if it can shoot as well as my other Winnys. Marine sniper Carlos Hath**** had no problem hitting at long range with his pre-64 Model 70 .30-06 on his first 'Nam tour and the other Marine snipers loved theirs. I really think the pre-64/Classic type Model 70 controlled-feed Mauser 98/03 Springfield derivative action is the ultimate reliable hunting action and the one that got the Model 70 the name "The Rifleman's Rifle". Their push-feed models are also the equal of any push-feed Rem 700. Sadly, with the closing of the New Haven plant (been losing money for years they say) the Winchester is no longer an option except on the used market. The Featherweight is my favorite M-70 version.
The Remington 700 is a nice rifle with a great trigger (new ones often need more work) and its cost-saving round action make it easy to bed and easy to make shoot well, plus they have good barrels. You can't go wrong here and is my #1 choice in the major rifle maker field with the demise of the Model 70. Yes, my two examples shoot very well when fed stuff they like (my '06 doesn't like lighter bullets.) I think the Remingtons have great aesthetics with a nice finish and decent stocks. I like 'em.
Third for me would be the Weatherby/Howa Vanguard/1500 with the nod going to the Weatherby version for some upgrades they insist on. A good action that is very nice and very, very accurate from what I have seen. Trigger is ok, but Timney can help you there. Nice choice of stocks and versions.
Fourth would be the Ruger M77. I, too, love the tang safety of the original M77 and the scope ring set-up. Barrels were outsourced on these for low-bid and quality varies a lot. My .270 M77 never will be a MOA performer, but is accurate enough for intended purpose. My .243 is very fussy but will shoot well with the right load. It has an extremely long throat. The new Mk IIs have barrels made in-house by Ruger finally that helps accuracy a lot. Their trigger drives me nuts, and the dished-out synthetic stock is the worst thing I have ever seen on a good rifle (but sturdy!) I don't plan on buying another Ruger however, even Mk II version.
Lastly would be the Savage 110. I had a Model 110 7mm Rem Mag that I struggled with. It exuded "cheap" and tinny. If I tightened up the middle action screw it would lock up the bolt. The trigger was thin and had sharp edges. The scope mounting distance was so long that I required a special mount to put on a Leupold 6x42 scope. When working up loads, top loads would give me .280 Rem velocities in the Savage chamber (a 7mm Mag issue with many rifles though). Accuracy was average only. However I think that a newer, more costly version with the AccuTrigger would be better, and a lot of people are very happy with these newer ones, especially heavy barrel versions. I was happy to sell it and get the cheap birch stock Win. Ranger that seemed to have much more quality and aesthetics all the way around, plus better accuracy. No more Savages for me however.