I have personal experience with the Reminton 700 and the Ruger M77 MK2.
They are both good rifles, but I liked the features on the Ruger better, its a very good Rifle, that will continue to perform under adverse conditions.
It has controlled round feed, with a masave extractor, and a Standing ejector, if you work the bolt hard it will launch your fired cases several feet away from you, but if worked gently will drop them in your hand.
It has a positive safety that completely locks the striker, one of the best safeties ever made, the integral scope mounts are rock solid, and their new barrels that Ruger makes, are of superb quality. The Ruger I own is my most accurate Rifle.
I recomend the Ruger M77 Mk 2.
The Reminton 700 was also a good rifle, although push feed, but functioned well and was very acurate, also has a very smooth operating bolt, or at least used too. Hope this was of help.
OOPS, I forgot to mention that I hunted for several years with a Savage 110 30 06 I took lots of game with it, and it was every bit as accurate as the Reminton 700 I had, the Stephens 200 that you listed is the same rifle, in a synthetic stock. This rifle would also suit you well, and not let you down.
My preferance out of the three I tested is still the Ruger though, that gun is awesome ! ! ! ! !