Most of what others have posted is correct.
I have done much of what the original poster has posited. I've loaded the .22Hornet down to .22lr levels (1.4-1.8gr of Bullseye), and to .22wmr level (4.5gr Unique, 6.2gr #2400, 6.8gr SR4759), with cast bullets; and of course 35gr V-Max to 3,200fps with 13,0gr Hod. Lil'Gun (however 11.8gr of H110 for 3,050 is much, much more accurate, as well as 9.0gr of #2400 for 2,900fps).
I'm still using some .22Hornet brass I aquired while I was in college in the '70's so the brass will hold up if not hot-rodded. Most loadings with this brass since the late '80's has been with the aforementioned cast bullet loadings and many are showing distress of cracking necks, but will still work for "mouse-fart" loads...
The .223 is indeed less expensive for factory loads, and more available, but is an altogether higher level of performance than the .22Hornet. The Hornet still has it's place and applications. The reduced loads is one of them.
Regarding the "Handi-rifle", I believe you'll be dissapointed. By spending a bit more for such as the Mini-MkX, or a CZ, you'll be getting a much better rifle. I lost a good bit of that batch of brass I mentioned above due to cases splitting at the ejector opening in the chamber of a "Handi-Rifle" I started out with back in '77. I aquired a T/C Contender in .22Hornet and quickly disposed of the Handi-Rifle. It had a sloppy chamber and the metal in the trigger works wouldn't hold a trigger job. It wasn't very accurate either, not enough to meet the demands of a Hornet on small non-game animals and fur-bearers I was using it on.
I didn't mention the .22 C-B cap equivalent loads I've shot many of.... A .22cal air-rifle pellet inserted in a primed case. With a CCI Magnum small rifle primer, they're suprisingly accurate and powerful.... Killed a beaucoup of pigeons while in college with those.