There is some thought a single stage press will give you more uniform brass, but I do know people who load 223 on a progressive and they seem to shoot just fine.
Uncle Don pretty much hit on the head but I will throw in some observations. The Redding match seater is a good one but won't stand up to compressed loads. I would recommend the Forster match seating die in stead. Some thing just better built. For the sizing die I use a Hornady match bushing die.
Uniforming primer pockets is a must. I also trim using a Forster trimmer.
I like and use Reloader 15. It's cleaner than Varget but I still believe in cleaning my rifle anyways. I also use Remington 7 1/2 BR primers. These work very well in a service rifle with it's free floating firing pin. In a pinch, there is not much group size change using CCI BR primers. I won't use Winchester or Federal Gold match primers as they don't stand up to the hard use of the S/R in matches. I know people use them but one of these days it will bite them at the wrong time.
God Bless our Troops especially our Snipers.