Adding to Tod's response, I totally agree that the 168-grain Barnes TSX is an outstanding all-around bullet for the .30-06. His load with 4350 is very widely used with that bullet weight, and it works.
Other excellent powders to try would be Varget, IMR 4064, Reloder 19, Reloder 22, H4831SC and IMR 4831, to name a few. All of these powders will give you decent results. (Personally, I like Reloder 22 and H4831sc).
My current choice, that works the best in my rifle, is more exotic, however. I use 64 grains of Vihtavuori N560, and get the best accuracy and velocity with that Barnes bullet (out of my Remington 700). This is the load that I would use for everything.