I am in the exact same boat as you. i just started getting into the long range shooting and hunting game. i want to be able to take it to the next level as well (400-800 yards). I also have a browning a-bolt 300. wsm but i just topped it off with Vortex Viper PST
4-16x50mm FFP sitting on some burris XTR and EGW 20 moa base. That was my major start to the long range business.
i know the browning's aren't the greatest long range gun but i know they will do to atleast 600 yards and im hoping to the 800 yards mark.
As for bullets, my thought would be the Federal premium 180 grain nosler accubonds.