My son is keen to do the 6.5 Grendel, long barrel and all, but I'm starting him off with 5.56. It's mostly Legos after that. I'd rather see the Grendel settle down a bit before jumping in. The 7.62x51 is incompatible with the AR15 lower, that will be an AR10. Ironically, the original Armalite AR10 (which lost to the M14) preceeded the Armalite AR15, which became the Colt M16, later to be retconned to the civilian AR15.
Anyway, I've just done with a .300BLK, which is 7.62x35, and uses the same .308 projectiles, so you can load some variety. Literally the only difference is the barrel. I'm not aware of a 7.62 bolt action for an AR15 lower, but I wouldn't be surprised. You can get a .50BMG one for (deity of your choice) sake.
Anyway, I've just done with a .300BLK, which is 7.62x35, and uses the same .308 projectiles, so you can load some variety. Literally the only difference is the barrel. I'm not aware of a 7.62 bolt action for an AR15 lower, but I wouldn't be surprised. You can get a .50BMG one for (deity of your choice) sake.