I use commercially cast bullets from Reed's. They are available in 37, 48 and 48 gr. weights and a couple different point styles. They are sized to 0.225" but that presents no issues with my rifle. If I were to try jacketed bullets, I would seek out the 0.222" for the Remington Jet or 0.223" for the early Hornets. Might take a bit of searching but they show up now and then. And, like Der Ami mentions, base your choice(s) on the results from slugging the bore.
My rifle was originally a .22LR so the bore is ~0.222" and the twist is 1:16 near as I can measure. For me, the 35gr. bullets shoot just fine but I have yet to try anything heavier. Sorry, I do not have any velocities to report.
My memory says (caution!) I used H4227 and cast bullet data from Lyman's Cast Bullet manual for the Hornet. I have several Hornets so I was at the lower end of the data in deference to the origins of the rifle and to sort of 'bridge the gap' between the LR and the Hornet.
