I've owned seven of them. They are great little truck guns, but I had issues with the wooden stocked ones - a 22 Hornet and 30-30. Just the luck of the draw. I had to play with the forestocks and ended up taking a little wood off and using nylon spacers on the screws. They shot okay after that, but it took me awhile to figure out. The best Handi I had, but foolishly got rid of, was a 308 Survivor rifle. I had too many 308s and that one got traded away. I'm carrying the 308 Survivor in my avatar pic.
I have three left, but they are all keepers, and all have synthetic stocks. A 44 mag, a 444, and a 22 Hornet. The 444 is a kicker and not particularly comfortable to shoot. I haven't taken this one out hunting, but it carries well. I cast bullets for the 44 Magnum and 444. A 255 gr. Lyman 429244 and a Ranch Dog 265 gr for the 44 Mag. A 325 gr. Lyman 429650 and Lee 310 gr. for the 444.
I never owned a 223 or 243 in a Handi. Just a couple of things with bottle necked cartridges when you're shooting them from a Handi. Headspace. When the shoulder moves forward and the action does not like to close, don't try forcing it shut. You are better off to invest in a Redding body die and pushing the should back so they will chamber.
And I wouldn't run any of the cartridges at maximum loads. The action strength is fine, but I have noticed that all my Handis preferred approximately 1.0 grain less than max. for best accuracy. Keeping the velocity down a bit also helps to reduce the forward movement of the shoulder.
I still use a headspace gauge for my 22 Hornet. If it fails - IOW, the shoulder has moved forward too much - I give the offenders a little squeeze with the body die. Straight walled cartridges aren't as finicky IME. It makes sense though. There's no shoulder to mess up the works.
This was my 30-30 (above). The stock was worked on. If JB reads this thread, he will recall when he tested a new Simmons scope, some years back. A 4x32. I believe he got a prototype to use. I bought a production scope. It truly was a POS. The reticle came loose inside and slowly started turning. The scope in the above pic was a replacement Bushnell 2-7x32 3200. I wanted to like that 30-30, but it gave me fits and I got rid of it too.
The last bit of strange is my Tactical Hornet. I was shooting this rifle with just a scope, but no bipod, cheek piece or "tactical" E-Z Pull trigger. It was shooting pretty good. .75 to an inch at 100 yd. My friend said I would shoot better groups with a CZ or even a Savage Model 25. I told him I was just breaking in the barrel and would be converting it to a "Tactical" Hornet. That's why I put the bi-pod, cheek piece and EZ Pull trigger on it. The EZ Pull has since gone away, but I kept the bi-pod, with the addition of a rubber pad, so that it would grip the forestock firmly.
The little Handis are fun to play with and shoot. It truly was a shame that they closed the doors there. You will get many years of fun with them. Just remember about the headspace and don't push the velocities too hard.