Primers for AR
The .223 Remington uses a Small Rifle primer. In a bolt gun you'll get good results from all the major brands: CCI, Federal, Remington, Winchester. The Rem 7 1/2s work very well with both stick and ball powders. Benchresters have shown a bias towards the Federal 205M (match), but in our informal testing, the CCI BR4s shot just as well as the Federals, while the CCIs delivered lower ES/SD with some powders. In fact, we've found that the "plain Jane" CCI 400s were closely matched with the much more expensive BR4s. Both can deliver good accuracy with low ES and SD. (Currently, at Powder Valley, CCI 400s cost $19.00 per thousand, while CCI BR4s cost $29.50 per thousand.) Some primers do seem to work better with particular powder/bullet combinations, so it's wise to do your own testing, and you may want to test CCI 400s vs. CCI BR4s head to head. You may find that the cheaper CCI 400s work just as well as the pricey BR4s in your gun.
For use in semi-automatics and AR15s, we advise that you stick to CCI and Remington primers. These brands have harder cups and are much less likely to pierce primers. Also, the AR15 has a free-floating firing pin that dents the primer on loading. This creates a risk of slam fires. So you want hard primer cups. The latest generation of Winchester primers, with brass-colored cups, should be avoided for AR15 use. The old silver Winchester primers worked fine, but the current WSRs are soft and can be pierced more easily than CCI or Rem primers. A poll of Highpower competitors (mostly shooting ARs) showed that Rem 7 1/2 primers are the most popular (33.23%, followed by CCIs (25.78%). The majority of CCI users favored the CCI BR4s, but both CCI 400s (small rifle standard) and CCI 450s (small rifle magnum) were also popular. Only 10.25% of Highpower shooters polled used Federal primers (either 205M or 205). At the time of the poll, many shooters reported using WSRs, but this was the older version with silver cups. See NationalMatch.us website for complete poll results.
I use the CCI 400 exclusively for my ARs and have never had a problem with them.
I use the CCI 34s (or that may be the number of the large ones, anyway the equivalent of the 34s) for AR15 loads, but those are just designed as plinkers/target rounds.
For any bolt gun I prefer federal match