As a go anywhere, do anything round consider a 140-145gr NP or Grand Slam in front of some H4895. Some folks say H414 is good too. I am currently checking out Varget (if the &^@#*! weather would cooperate).
Since moving to WV, I have been using a 154gr Hornady ROUND NOSED bullet with good success. At the shorter distances here, it has done very well. I did shoot one deer at 240 yards with it and didn't feel handicapped doing so. It was one of those "bang flop" things that folks talk about but one deer doesn't mean a whole lot. I have never shot a bear but I would think this bullet would do well for them.
If this is your first 7-08, you're gonna find that it is pretty easy to get along with and will do well with most any reasonable load you want to use.
BTW, that sounds like a fine, balanced rig you're getting.