I would like to follow up on my earlier comment about the Hornet rewarding careful case preparation. I sort cases by weight and use only a narrow range when loading for accuracy. I debur the flash holes. I measure the case neck thickness with a Sinclair gauge and use only cases with even measurement all around. I neck size only, and I weigh every powder charge. I keep cases trimmed to uniform length. I measure COAL for each bullet used with a Stony Point gauge, now sold by Hornady, so I can experiment with different bullet seating depths. Close to the lands usually works best, as popular belief dictates.
This sounds like a lot of busywork, but the smaller the case, the more important is case preparation, and the Hornet is about the smallest case you will find. With a very small case, "normal" variations in case or loading parameters have a much bigger effect than they would with, say, a .30-06. I once bought 100 WW Hornet cases that showed a weight variation of 8%!!! If you have Hornet that does not shoot, try these things before giving up. It it sounds like too much work, then find a .222.
I am happy to see there are some Ruger No. 3 fans here, but if you find a used No.3, it will carry a hefty price tag. So will a Winchester Model 43, which is much less rifle, IMHO, because of what Winchester lovers are willing to pay. For roughly the same dough I would take home the No. 3. A Browning 1885 Low Wall would be great, and I think right out of the box the Low Wall might do better than a No.3 because of the way the 1885 attaches the forearm. After finding the right load there won't be much difference. Failing all of these, I would go for a CZ, or, feeling rich, an Anschutz.