As a rule, mix'n'match of components doesn't affect the basic function of the ammo you make.
But, the type of thing you need to be cautious of is ... one brand of brass may be heavier that another brand and since they all pretty much abide by SAAMI dimensions on the exterior, that would mean some differences on the interior. Like thicker walls and web. It may mean a several percent reduction in powder capacity. That would have quite a few possible impacts.
The best thing to do for a lot of reasons, not the least of which is your piece of mind, would be to stay with a basic "recipe" and only vary one thing at a time as you progress into reloading.
Start with a brand of brass, primer and bullet of choice. Then choose the powder(s) you want to experiment with and don't change anything in your load but the powder. Once you decide on a powder you prefer for a given cartridge, you're set. If you decide a year or month later to use a different brand of primer, for example, you're back into the experimenting mode.