I have a Winchester model 77 too! This is the model of gun that my father taught me to shoot with and I am really fond of it. The one we owned was stolen, so when I saw a used model 77 in a gun store in 1986, I jumped on it. I have more accurate .22 caliber guns though.
Remington 582 first and Marlin 39a second in my experience. The 582 was 5 shots into a dime on a good day and a nickel on a bad day from a rest at 50yds w/ a 4x32 scope and a joy to carry. Squirrels and foxes hated that gun!
Marlin 49DL. I put a lot of rabbits on the dinner table with it. I still have it. I can't remember not having it. (I also used a Mossberg 183K .410. I sold it to get a car in the mid 70's. I still look for one at gun shows.)
CZ 453 Varmint (the one with the set trigger) with a Burris 3.5-14 scope. My dad's old Remington 341P (1938) is close but limited by the trigger and peep sights. The CZ shoots well with most ammo but really likes Eley Match. From the bench, we chase 45ACP brass around the berm @ 50 yds. (fun isn't it, Vern?)
Believe it or not...back in the late 80s I owned a (then) Charter Arms AR7 takedown rifle ( now made under the Henry brand)...my brother-in-law said it was junk but once I got it and found the right ammo, it was a tack driver. Wish I still had that one.
Those rifles are the best Bug Out Bag rifles you can buy...ammo is cheap and affordable...can survive and feed yourself and family on rabbit, squirrel, small - medium game with great head shot placement . Fits in a BOB .
I can't stay away from a thread that has .22 rimfire in the title.
Got a new "most accurate" recently. 1885 low wall reproduction. Inside a dime at 50 yds with my homemade wolf match target hollowpoints. Think I can kill squirrels at 100 with it.
The most accurate was probably the mint Mossberg 144LSB I hunted with for awhile back in the eighties. It was all original (including the front sight inserts) and weighed about 14 lbs fully set up. Had the factory sights PLUS a Unertl 10X scope and blocks. Shot like a dream but what a pain to carry.
Years later I had a Ruger M77 .22LR that had been worked over by one of the better known gunsmiths. It was absurdly accurate, but didn't have anywhere near the ergonomics/steadiness of the Mossberg.