The common reloading manuals show Magnum primers for the 300 Win Mag, especially with slower burning propellants. The Speer #14 manual obviously recommend CCI250, the Large Rifle Mag primer, which is also what I prefer to use in my 300 Win Mag, 300 H&H mag and my 300 Ruger Compact Mag.
Also remember the general idea that a cartridge using 60gr or more propellant, will give better, more consistent ignition with magnum primers, especially if you hunt / shoot in colder weather.