Garrett - cartridges like the mellow little .308 Win are typically very easy on barrels. The last Krieger I had on my LR match rifle went 5600+ rounds before I wasn't satisfied with the accuracy. It went slowly, the groups just gradually opened up at 600 yards, and there wasn't anything I could do about it at that point. When we pulled it, there was pretty bad erosion the first few inches out from the chamber, but it was still shooting 10's at 600 yards, just not many X's.
Some barrels reportedly die pretty abruptly.
The high-velocity cartridges, burning big quantities of powder, do tend to wear a barrel out pretty fast - but if it's a hunting rifle and you'll only shoot 100 rounds or so a year through it - that could be 10, 12 or 15 years of shooting!
If it's a rifle for NRA highpower competition, you're toast in a season, or a half a season!
Avoid heat-makers, like rapid fire strings... Shoot a group, then let the barrel cool. In competition, I have to shoot rapid fire strings and I'm sure that's death on my barrels...
Clean gently - and really, a good quality barrel like a Krieger may not need much in the way of cleaning. I generally get by with a couple of wet patches, let it soak, then dry it with a few more clean patches. All done. Fouling is gone and the rifle is ready to go again.
Most custom barrel makers will have some sort of break-in procedure they recommend. Not usually very hard to do at all. A few shots, some cleaning and presto, the barrel is properly broken in. How do you know? When you can shoot a lot of rounds, accurately, without excess barrel fouling. I generally get a fresh barrel all broken in and good to go in about a half an hour and a dozen shots or less.