I recommend the NF 5.5-22x 56mm; 8-32x 56mm may be better depending on your preferences. Cheek weld depends on the rifle. The two rifles I have one on I have no problems with it. I like the Barrett EX Rings. Light for their size, but super wide and strong. I can vouch 50bmg is no problem with this combo, so I doubt 338AM would be.