The '06 should be fine for your purpose. In my opinion, and I am by no means a long range competition / benchrest shooter, long range hunting / shooting is a matter of shooting a rifle that is known to be accurate and shooting it well. The easiest way I've found to gain confidence is with a big target. I have a 22" farm disc hanging on chains that I can shoot at from almost any distance out to 900 yards. I've used this for my own practice as well as introducing new people to the challenge of long range shooting.
My dad had never shot much past a couple hundred yards - last summer we got a good load worked up for him, and I used the Gunwerks ballistic chart to get his drops figured out. His first shot at 550 yards was on target (he doesn't smile like that very often).
Now, I'm not by any means saying a hit on a 22" target should give anyone the impression that they can go kill a deer at that range. It's all about practice. A big target will help you "walk" shots in while trying to learn how to dope wind. Elevation is the easy part, it's the windage that you will find that makes things difficult at extended range.
And, practice as much as possible from field positions. The only time I use a bench is to see the real difference between loads at short range (100 - 200 yards). There are a lot of very knowledgeable folks on this forum (much more knowledgeable than myself), so take in as much as possible. I learn something just about every time I log on.
In the end, long range (non-competition) shooting is about shooting a good rifle well and knowing your capable range.
The hardest part is the addiction!