I have one of the older Lone Wolf .40/9mm conversion barrels for my G22. It has given me great service, but I think they have changed barrel makers since mine was purchased, so take that into consideration.
I've always been a fan of KKM barrels. Had one in a G-22 before I sold the pistol to a friend who had to have it and currently have one in the G-21 that is my nightstand gun. Excellent quality, accurate and handles my handloads well.
My 9mm conversion barrel for my Glock 35 was also by Lonewolf, and, from 7 or 8 years ago, and, works great...(The tighter chamber tolerances did have me shorten my OAL by a few thousandths down to 1.12" or so to prevent shaving bullet coating, which seemed reasonable)
KKM has the longest throat, so will be the most forgiving if you want to run your own longish reloads.
If you are running factory ammo, pretty much any of the name brand barrels will work fine, KKM, Storm Lake, Lone Wolf and Alpha Wolf, etc.
You can usually find used Lone Wolf 40 to 9mm conversion barrels on EBay. $60 seems to be the going rate shjpped. Hard to wear out a barrel, so I would look there first.
PS - try it first with your G22 magazine before buying 9mm magazines (if you don't already own them). My G35 with its Alpha Wolf conversion barrel actually feeds better with G22/G35 magazines, than G17 magazines.