One of my favorite rounds! I've got two rifles and a TC Contender pistol. Like others, my first rifle was a Hornet.
It's a good, quiet, economical round. Hornady loads their Ballistic Tip round for it, advertising around 3000 fps in the 33 grain bullet. Which is about max. They use, I"m pretty sure, Li'l Gun powder, which is what I use for mine. It's knocking on the door of 3K, if it's not there. Don't have my data with me and can't check.
I've got a Brno Fox, and a 77-.22 H in the rifle category. The 77-.22H is very accurate, making it a ~ 200 yard gun for small varmints and with the right bullets. I haven't grouped the Brno yet, but had one before that, when bedded, would do 3/4" most of the time.
The very old ones, pre-1950 or so, were .223 rifled, but that's history, probably since the .222 established .224 as the standard bore for .22 caliber. I don't think you can find loaded ammo in .223 bullets any more, but you can buy them at reloading sites.
They used to sell "Hornet bullets" in .224 which were very thin-jacketed to expand at the Hornet's modest velocity.
IMR 2400 is a good powder, developed for the Hornet to give 2400 fps with a 45 gr. bullet, hence the name. Not as good as Li'l Gun in my rifles, but there it is.
You can get maybe 500 reloads from a pound of powder, making it a very cheap round to load. The .222 and .223 dampened enthusiasm for the Hornet, but it's still popular here in the US and quite popular in Europe for hunting chamois and other stuff in that ballpark. The problem with cutting edge accuracy is because it's a rimmed cartridge, which makes those gilt-edged gropes harder to find.