Yes primers can effect accuracy and in some cases fowling conditions in the rifle. The usual rule of thumb is, if you start with Winchester, then try to stay with them. I use Winchester primers and have good luck with them. I also shoot Remington Kleenbore primers and they work good.

Some good primers are Remington Kleenbore Primers, and Winchester. Also Winchester came out with a primer called Winchester 777 but I have not tried them yet.