Yarn Yarn. Same old same old.
.20 is unnecessary and almost pointless.
For the flattest trajectory, tightest groups and more success on a FT/HFT course you choose .177.
For hunting of any power level, accuracy kills not size, so again the most accurate calibre, smallest groups etc .177 under 12ftlb.
FAC air .22 or .25, but I don't really see the point. If you need more range than FT ranges then use Rim or HMR.