Federal primers are good, but so are the others. My first choice in almost all my loading is Federal, with MagTech second. Then comes Winchester, S&B, Remington and CCI. I refuse to buy anything made in Russia, since I grew up in the 1950's, when they were going to incinerate us off the face of the earth and bury us (Nikita Khrushchev).
They should be stored where it's cool and dry for the longest shelf life, as well as powder. I'm fortunate in that I live where it very seldom gets above about 75 degrees F in the summer, and winters are pretty mild, but wet. I'm still using primers that I bought in the 1970's, and have yet to have one fail to fire, but they've been stored under just about ideal conditions for as long as I've owned them. The same with powders that I bought back then. I'm still working on a 12 pound metal keg of SR4756 from the same period.
Hope this helps.
Fred