Kristian,
i agree with Calhoun - shot placement, practice practice and then some more...
Every owner of a rifle can respond on his / hers favorite caliber to be the best all-rounder.
What i have found during my hunts in Namibia and South Africa, and maybe this may come in handy for you too, whether you have a rifle allready or whether you are going to get one, first of all ask yourself these 2 questions:
• "what am i going to hunt regularly?" (smallest to largest)
• and "where am i going to hunt it?" (dense bush / plains/ mountains)
When you have the answer to these two questions, your outfitter (or even the guys here on AH) will be able to guide you to a appropriate caliber / load
Yes the 30-06 is a proven all-rounder. I myself have one, but i also have a 270. I have zeroed my sights with 180 gr bullets on 100 m with the 30-06 which i use exclusivelly for hunting in moderatly to densely vegetated areas, and zeroed my 270 with 130 gr bullets on 250 m for longer shots in sparsely vegetaded areas - i find these two rifles does it all for my hunting purposes locally. Having these two rifles means i do not have to switch loads and re-zero on every hunt.
I always ask the farm owner / guide before hand (when booking) as much about the terrain as possible before i go hunting - this guides me to decide what rifle i am going to use. (pending on the size game as well)
However, should you have only one rifle, (30-06 in your case) and you are going to hunt in dense bush-like country - get as much information about the topography and sort of vegetation at the place where you are going to hunt. Enquire from the landowner / guide about the maximum and minimum distances you will probably shoot, and zero your rifle accordingly with the appropriate bullet gr. and practice, practise, etc. Same goes when you are going to hunt in open plains - the same as above applies.
This worked very well for me the past 28 years of hunting.
Hope it helps you as well.