Tom, first off, welcome to the forum! Always glad to see a new member to our family. Please feel free to ask anything that you can think of in the way of firearms and we'll do our best to help you out.
Now, as far as your new .22 purchase, I've got a couple of tips for you. I knew a group of a couple dozen .22 shooters that used to shoot bricks of ammo at a time and the good shooters used to approach just over 3/4". The problem is they were using rifles like Anschutz and Kimber, real high-end stuff. The one Ruger in the group was custom: a 77/22 with a stainless Lilja barrel and a custom 2 lb trigger. There was a 10/22 that had the trigger pull lightened with a Volquartsen hammer and the chamber and barrel had been accurized. This custom work was what was required to get under 1" at 100 yards - this is a sub-MOA gun which will always cost some money.
Every .22 shooter I know had to find the ammo that worked best in his weapon. There is no shortcut to this. You haunt gun stores, sporting goods stores, big box stores, order it online, search through Shotgun News and find every brand of ammo you possibly can. Hyper-, standard- and sub-sonic velocity are all a possibility. light and heavy bullet weights. Standard and match grade. You will be surprised what something like Match grade Lapua .22 rounds will run you Lapua X-ACT
but they will usually match up with a match-quality barrel quite well. The problem is that ammunition is probably the BIGGEST influence on accuracy and group size in a .22 rifle. There is no substitute to buying hundreds of each round and shooting them under controlled conditions to find out which is the very best in YOUR gun.
Finally, make sure when you buy a scope that it is a RIMFIRE scope. Most centerfire scopes are parallax-adjusted to 125-150 yards, whereas rimfire scopes are parallax-adjusted at 50 yards. This is a huge difference and can keep you from having any sort of true accuracy if you aren't seeing the target correctly. Also, you might consider a fixed power scope, like a 4X, so that after the scope is adjusted to center at 50 or 100 yards, you can just bring it to bear and won't be playing with adjusting the power.
And just my .02 - I have a Ruger 10/22 (non-HB version) that is decades old and is deadly accurate with CCI ammo. I wouldn't trade it for anything if my life depended on it.