There are very few shotguns that will not shoot slugs. Make sure you do not get one with a Damascus steel barrel. Doubtful if you will even see one tho.
INMO, a Ruger 10-.22 is the best considering price. Very reliable, very accurate with the right ammo. Mine is a constantly accurate rifle out to 120 - 130 yards. Beyone that takes some luck. If I could only have one rifle, it would be a 10 - .22
I bought my 10/22 brand new for around 40 dollars.
This is where the "blossomed" barrel you see in cartoons came from. (Mythbusters, naturally, screwed up this story when they were playing with a-finger-in-the-gun-barrel myth)
I recall, vividly, all the warnings in American Rifleman, back in the 50's. Guns last forever, and hauling GrandDad's side-by-side Iver Johnson goose gun out of the back of the closet and loading it with modern shells was a fairly common mistake, then.