Buy AR 500 plates of the proper thickness for the caliber and don't shoot them closer than intended. That way they will not be damaged and won't send fragments in directions not intended. Hang them loose so they can swing and waste/use up a lot of the energy before the steel has to absorb it.
Don't cheap out, use AR 500.
Pistol:
25 yards or less? 3/8" AR 500 will withstand up to .44 Mag.
50 yards or more, 1/4" AR 500 will survive up to .44 Mag and rings better than heavier plates.
Rifle:
No less than 100 yards and no less than 3/8" AR 500. Thicker for fast stuff. Speed kills plates. Even 1/2" can suffer at 100 yards with things like 7MM Rem Mag. Again, hang it loose to absorb energy moving the plate before the plate has to eat the energy. One of my sons shot holes in my 50 yard 1/4" AR 500 plate with a .223, despite me telling him no less than 100 for rifle and no less than 3/8" at that distance for rifle. *Sigh*
Heavy hitters (Like your 338), especially speedy ones, 200 yards minimum, at least 3/8" and 1/2" is better.
Now, folks will tell you this is over kill, and they do X, Y, & Z all the time. More power to them.
Stay safe.