Hornady makes .312 size bullets in 150, 174, 180 and 190 grains.  The 174 grain bullets are the normal size for both the .303 British, AND the Japanese 7.7 Arisaka.  If you only intend on shooting Paper, IMHO I would stay away from heavier rounds and stick with lighter weight bullets.  My normal target load (I no longer hunt, and only shoot paper) is a Hornady 165 grain boattailed spitzer loaded with 38.6 grains of IMR 4064.  My velocities are around 2200 (guestimated) and my pressures remain relatively low...  And pretty deadly accurate at 100-200 yards. 

IMR 4064 is a medium burning powder that works very well with 150 to 180 grain bullets, and I use this in my 30-06 reloads for my Garand Rifle too!  What every powder you wind up using, be sure to consult a good reloading manual to work up your loads.  A good rule of thumb is to stay below max loads.  I try to stay 2 below max for my bullet weight and powder, just as an added safety measure, and my accuracy hasn't suffered yet.

As for brass, it's a wash.  Either brand will work equally well.  The only thing I can think of to note is that Winchester brass cleans up nicer than Remington.  Remington brass sometimes tends to be darker in color and tarnishes easily. 

Happy reloading!
Paul