.308 is intermediate. It is the best calibre on most game international speaking. Accuracy as well as availability are great and there's variety on bullets.
I'd go for anything like 7x57R, .308 or 8x57 IS on every mid-sized game worldwide.
For larger game, a.k.a. big game i'd reccommend 9,3x62. It was developed as an african calibre. It's suited for buffalos and elephants. Being as powerful as 375 H&H it is still smaller.
For reccomendations: I'd take a quality bolt action rifle like from Heym. Take some intermediate calibre like .308 or the ones above. Have one back up rifle in 9,3x62 or larger for dangerous game. That's all.