There are several makers of brass, boxer primed cartridge cases - Prvi, Sellier & Bellot, Norma, etc. Google 7.62x54R Brass and see what pops up. Or buy some brass boxer primed ammo, and save your brass.
As RJ said, some will give decent accuracy with .308, most are going to go better with .310. You can also find cast bullets that will give you lower costs- keep your loads reasonable for a cost boolit, you may be surprised.
You can definitely reload the caliber- I personally would not attempt to reload the steel cased berdan primed milsurp cases unless I had to.