I found with RnRC that my neck feels better if I DON'T try to stiffen it or brace it against the headrest, but instead relax the neck muscles and let it roll around slightly within the headrest. The whole ride becomes more enjoyable this way. Note, I mean relax it against the headrest, not relax it holding your head erect away from the headrest.
On Revenge of the Mummy at Universal I found on the other hand that it's best to brace my head against the headrest - at exactly one key point in the ride when it suddenly whips over sideways (or something). Only by bracing it at that exact time could I avoid the uncomfortable feeling of side-whiplash. Mind you, you have to ride it several times to learn where that point is!
Although Everest is scary and extremely disorienting (in a fun way) when it goes backward, it doesn't have a bad physical effect on me (so far, touch wood). The looping coasters at Universal/IOA, Seaworld and Busch Gardens mostly give me headaches, nausea or stiffness. The baddies are: Hulk, Dragon Challenge, Kraken, Manta, Montu and one more green-colored and fairly old-school looping coaster at Busch Gardens. The goodies with inversions are: Rip Ride Rockit (technically you're not inverted 'cause it flips you right-side-up at the top of the loop), Sheikra (very fast and smooth and only 1 large inversion IIRC), and RnRC as mentioned. Haven't been on Cheetah Chase at BG.