Usually the powder containers themselves don't specify what primer to use.
However, the load data provided by the powder manufacturers and the bullet manufacturers almost always provides the primer brand and type used to create the loads that were pressure tested. It is best to try to duplicate the primer/powder combination of whatever data you are using, including the BRAND of primer.
There are occassionally bits of data published to show the potential problems with switching primer brands. In the most recent edition of Handloader Magazine, some data from Western Powders was published showing the following with a "Ruger only" .45 Colt load using a 310 grain cast lead bullet and 21.0 grains of Enforcer powder:
Primer Velocity Pressure
CCI 350 1,352 fps 35,950 psi
Rem 2½ 1,238 fps 23,990 psi
Win LP 1,239 fps 22,490 psi
Fed 155 1,278 fps 27,870 psi
So, substituting a CCI 350 primer in data developed with a Win LP primer could increase this particular load's pressure by more than 13,000 psi. That is definitely not something that you would want to have happen if you were shooting one of the Rugers built on their mid-sized "Flat top" frame instead of one built on their large frame. In this particular load, the 100 fps increase in velocity should be a tip-off that something is not as expected. But, such velocity increases are not always so apparent when there are substantial pressure increases. And, not everybody is using a chronograph so that they would know that there was a velocity increase.
So, start with primers that are used to create whatever data you are using, rather than experiment or take some store clerk's recommendation.