Best ammo for the 'A3 is the same as the best ammo for any rifle, its the reloaded ammo tailored for that gun.
If you don't reload, then it depends on what you do with the rifle. If you're plinking and want "good" quality yet inexpensive ammo the the Surplus Ammo from the CMP is the way to go. Good enough for the CMP GSM Matches that are shoot to 200 yards.
If you want quality target ammo, Hornady makes Match '06 for the Garand that also works great in the '03s. (Also sold through DCM).
If you want hunting ammo, then just about any of the commerical stuff you find will work. As mention, get a box of each and try them.
People talk about low pressure '06 ammo, that is because of the gas system of the Garand. The "03's don't have that problem, they will handle any of the commerical stuff out there.
Personally I like my reloaded stuff the most, I don't hunt with my SC 'A3. Its for the GSM matches. I load 110 Hornady bullets, quite mild, easy to shoot, inexpensive, and supper accurate in my 1903a3. (also works the action in my Garand).
I even use cast bullets for cheap practice shooting offhand at NRA 50 ft small bore targets.