As a gunsmith in the center of Wyoming I get to see what the most common rifles and calibers are on a common basis. Without a doubt the bolt action is most common and the 2 most popular cartridges (by far) are the 30-06 and the 270 Winchester (no one is likely to be surprised there)
In a close 3nd place is the 300 Win Mag and if I were to guess I'd pit the 7MM Rem mag and the 25-06 in a tie for 4th place.
By guess at 5th place is a mix of many shells. 25-06, 243, 6.5 CM, 280, and probably a small batch of others are in that bag.
Just below that placement are the 338 Win, the 300 Ultra mag, 6.5X55 Swede and the 45-70 as well as the 375H&H. This category are the ones that are not near the top, but not a surprise at all when you see someone hunting with one.