I do quite a bit of .303 reloading. Your best bet for brass is to buy a bunch of Prvi Partisan ammo and reuse the brass. It's also sold under the Hot Shot brand, which looks like El Cheapo no name stuff, but it's still quality Prvi ammo. Unfired brass is hard to find. PRVI will have a PNY or PPU headstamp.
The .303 and all other rimmed cartridges headspace off the rim instead of the shoulder. In the case of the .303 Brit this can cause trouble for reloaders, because Enfields typically had very generous chamber dimensions. The shoulder in an Enfield chamber is usually much further forward than specs called for. They did this to ensure reliability if the rifle was dirty. What this means for the reloader is the brass stretches a LOT on firing. If you compare a once fired .303 case to unfired factory ammo you'll see that the shoulder moves way forward. This stretching causes the brass to thin and will eventually lead to case head separation, sometimes after only a couple of reloads.
The way around this for a reloader is to neck size your brass. Get a neck sizer die and only resize the case neck, without bumping the shoulder back. This prevents the case from stretching repeatedly after that first firing sizes it to your chamber and will dramatically increase case life. The downside is if you have multiple guns in the same caliber - you may only be able to use neck sized brass in the same gun it was originally fired in.
I have had very good luck with a mild load of H4895 and cheap Russian pulled 147 grain .311 bullets. I'm getting about 2.5 MOA in my No. 4 MkII, which is pretty good for a surplus rifle. Quality bullets will probably shrink those groups quite a bit. I'm planning on buying a mould and trying to cast some bullets in this caliber, since I somehow keep accumulating .31 caliber rifles.