congrats on getting that ol chuckster, they are a fine 22 mag.
first, pitch that scope and put something better on it, get some weaver rings.my own suggestion would be to get the scope in the rings,slide it onto the grooves and loosly tighten the rings.get it where its level and apply a drop onf locktite to the screw threads.,use the blue loctite.red is hard to get loose without heating it.recoil isnt going to be a problem but keeping it from moving is why I use loctite.just added security from things that bump it.
the other suggestion is check the barrel channel.the sling screw might have been turned(overtightened) a bit too much, if th3 tip is in the barrel channel, itll throw your shots.you dont want anything touching the barrel cept the stock.if youve done everything you can do and it still shoots bad groups, there may be other issues in that gun such as bad barrel or barrel crown damage.
I used winchester hollowpoint in the one I had but with todays variety, you can try any number of offerings.find the one that gives you the best group size then stick with that.
almost forgot, you can test the gun without the scope to see where its hitting and its consistancy before diagnosig a scope/gun issue.if its ok with the irons, scoping it should work out great.hope your gun works out, chucksters are one of my all time personal favorites.
p.s. had a bushnell 3-9x sportview on my ol chuckster...my current centerfire varmiter sports a inexpensive tasco 6-24x,its held zero for at least 15 years...never shifted.
good luck.