I'd start with 5.56 in 1:7 twist bbl. for maximum versatility. Next I'd go to .22 LR for ultra cheap plinking, training, short range practice; basically everything you'd use any other .22 LR rifle for.
For a third caliber I'm leaning toward .300 AAC Blackout myself. 30 caliber bullets in necked up standard 5.56 brass (which also means it uses standard AR mags & bolts), with heavy backing from AAC & Remington (and the massive Freedom Group to which they belong) are why it appeals to me.
6.8 SPC is neat, but you can't form brass from anything else, and good mags for it are expensive. It does have good backing from Freedom Group though.
6.5 Grendel may be the best of the medium caliber AR-15 compatible cartridges, but Alexander Arms is controlling it so tightly that it's basically proprietary. 6.5 Grendel is the Beta Max of rifle cartridges. The 6.5 Grendel's parent case is the 6mm PPC, which has 7.62x39 as its parent case. So, you can make your own brass, but good mags will still be expensive & hard to find.
Between .458 SOCOM, and .450 Bushmaster, it just depends on preference. Some like the .450 BM for its .452" diameter bullets that are cross compatible with .45 ACP & .45 Colt for handloads. Others like the .458 SOCOM because there are more heavily constructed .458" diameter bullets for heavy game hunting. These bullets are also compatible with .45-70 Government, and other large game rifles.