If you want low recoil for follow up shots, 300 BO, 6.5 Grendel or 6 ARC. The only accurate shot will be the first and follow ups will be on runners. Even suppressed, after the first shot all bets are off.
If you know you will have 200+’yard shots and you are buying a 640 or better resolution thermal then I MIGHT consider an AR10 class rifle. But it’s going to suck carrying it very much. I think you get better bang for the buck with an AR15 in the chamberings mentioned above.
I’d shoot a 100-120 grain bullet either a mono or tipped lead core. Nosler Varmageddon Hornady Vmax do well at Grendel and BO velocities. TTSX and TAC TX do well as well.