I would say you are dead on with your choice. It was going to be what I recommended from just reading your title. I chuckled when I opened your thread and saw you were already thinking about the 338-06.
As far as bullets are concerned, nothing wrong with using a close range and a LR bullet but I think you may find that in 338 it isn't needed. There are some really good bullets in 338 that I would feel very comfortable with for close range protection against a predator and for LR precision use on big game. The Swift 210 would be one, followed by the Hornady IB and Nosler AB. I believe they all have BC's around .51 and perform well on game under a wide range of velocities.
The thread below was a good one for info on the 338-06 and also the AI version. Lots of good info and comparisons.
338.06 VS 30.06 Ackley