>> Everything I'm seeing is saying .220 Swift or 22/250. In so much than apart from "class", I'm
>> not sure you’re actually achieving anything.

> The reason is the rifle will be a break open type rifle which could not handle the pressure. Plus
> I want a rimmed case.

The H&R Handi Rifle is available in 22 Hornet (a rimmed cartridge), 22-250, and 223 Remington. In addition, if you want a little more power, it is available in 243 Winchester, which handles a 70 gr bullet rather nicely. I own several of these rifles, and I'll be the first to admit that they are not particularly "classy." On the other hand, for a base price of 250 USD, you get a strong action, an accurate barrel, and a trigger that can be made pretty good. Mine are very accurate. By removing one forearm screw you have a take-down rifle, and mine returns to zero on reassembly rather nicely. I sewed a roll-up case for my 270 Winchester Handi Rifle using a large beach towel as raw material. It has three pockets, one for the barrel (with forearm attached), one for the scope (in ordinary Weaver rings), and one for the stocked action. For one year I took it to the range once per month, assembled it, and fired one shot at 100 yards. The composite group was less than two inches. In my book, classy is as classy does.