I've had one in .22lr, and still have one in .17HM2. Both are very capable of well under an inch at 50 yards. The .17 is sub-MOA at 100 yards. The .22 was never shot at 100, but would group several loads (especially Rem Subsonics and Winchester Powerpoints) into 5/8 inch at 50 yards. These are accurate little guns.
The trigger on my .22 was not as light as that on the .17, but still quite shootable. My .22 came with open sights, but you can get a cheap Weaver-type rail that comes with a hammer extension from H&R. Any decent .22-type scope (i.e. parallax set at 50 yards, or with adjustable parallax) will work, but you usually need to use fairly high rings due to interference with the hammer. This is a pain with all the H&R single shots.
Go to Graybeardoutdoors.com for tons of useful information on these guns. Those guys are rabid H&R fans and very helpful.
John