I would skip the military surplus brass if it's going to be dedicated to a precision bolt action. Surplus brass will always be my first pick for a semi-auto but it really isn't as consistent as Lapua or Winchester.
It also severely limits velocity when compared to commercial brass. You can safely go 50 fps to 100 fps faster when running commercial brass. Federal brass is notorious for being soft, but it can usually be found once fired because so many agencies use it. 41.5 grain of IMR-4895 and a 168 grain SMK will shoot great from most bolt actions when using it. 42.0 to 42.5 grains of IMR-4064 also hammers with 168's in Federal brass.
Don't expect many reloads in Federal brass if you decide to hot it up.
Lapua is the best and it is almost always available. Expect to pay 70 cents for each case give or take. Winchester commercial is almost as good as Lapua and will perform admirably if you uniform the primer pockets, de-burr the flash hole and separate the resized and trimmed cases by weight.
Lake City cases almost always shows unacceptable run out because of uneven thickness in the case necks. They will perform just fine for practice and anything inside 300 yards, but if you actually plan to compete at 600 yards or further you will be disadvantaged. If you just want a quantity of useful ammo for 90% of your shots the Lake City will work fine.
I use 40.5 grains of IMR-4064 under a 168 grain SMK when loading Lake City or IMI brass. It performs acceptably well from several rifles and exhibits no pressure signs. The NRA performed pressure tests using Lake City brass and my IMR-4064 load is 1.0 grain under their maximum load listed. YMMV.