AR cartridge suggestions
"Question: What would you reccomend and why?"
What I always suggest is that you start with an AR-15 in .223R/5.56, preferably with the .223 WYLDE chamber.
Since you have that covered, next suggestion would be a .22LR CONVERSION UNIT instead of a .22LR upper.
After that would be the 6.5X38mm Grendel.
Finally I'd go with a "large bore" AR-15. These are the .450 Bushmaster, .458 Socom and .50 Beowulf.
Any of the 3 are good choices depending on your needs.
Both the Bushmaster Beowulf use HANDGUN bullets.
Since I was looking for a "rifle" I went with the .458 Socom. It uses .458" RIFLE bullets from 250g up to 600g. Since I already have a .45-70 and .458 and plan on adding a .45-110 this simplifies bullet selection. And, if needed it could use the smaller .451/.452" handgun bullets.