In my opinion, the ultimate "classic" rifle action came out of Paul Mauser's factory in Oberndorf, Germany, in 1898. That version of his many bolt action designs spawned, parented, or made folks think more about bolt actions than any other since. It's still available in different sizes from different companies and its fundamental design's not changed.
The US military folks paid Mauser a generous amount to use several of its patented features in the M1903 Springfield.
Winchester commercialized the 1903 Springfield design for their Model 54 in the mid 1920's.
Winchester improved their Model 54 in 1937 with the Model 70. No other box magazine rifle proved as reliable, easy to maintain, repeatably accurate in competition and overall performance in sniper use than this one.
Too bad Winchester was in financial straits in the 1960's when Uncle Sam wanted a new sniper rifle. Virtually all the top rifle competitors on military teams wanted the Winchester for sniper use (many of them were snipers). They knew the problems with the Remington 700's were hurting its reliability and it was not favored for competition with heavy recoiling cartridges in spite of its success with mild rounds in benchrest matches. Note the Rem. 7XX's are decendants of the 1917 Enfield rifle; 1917 fathered the Model 30 which fathered the Model 720 which begat the 721/722 and finally the 700.
But I digress. Back to the original "classic". . . . . .
The Mauser action of 1898 is, without a shadow of a doubt, the best bolt action ever invented. Copied by dozens, used by millions and coveted by collectors the world over, the Mauser simply keeps on doing the job in spite of its old-fashioned looks and a whole legion of grandiose claims from a bunch of wannabe successors, all of whom seem to fall by the wayside one by one as time goes by.