I would slub thre bore to determine exact groove diameter. If it is .222" or .223" you can use .223" diameter Hornady or Speer bullets. If it is .223" or .224", you can use standard .224" or .223", whichever is most accurate. Only testing will show.
; The standard Hornet chambing is the one I'd go for and you can load it as originally loaded with a 45gr. bullet at 2,400fps, the same bullet at 2,000fps or 40 to 50gr. at 2,700fps. Prsure is what you load for it. Do not shoot factory ammo unless you've satisfied yourself that the action will take 44,000CUP. In Europe, the Hornet is loaded to lower pressure than in the States.
; Break-Open Rook rifles may not have the locking strength for full powered Hornet loads. The .22 Rim fire mag and .22 LR both produce 24,000 to 25,000CUP breech pressure.
; Tread carefully. I would not consider the larger cased rounds like the .22 HiPower. The other choice, .25/35 would be fun with cast bullets only, but it is also a 40,000 CUP round with jacketed, no different than a .30/30.