For fun & target you might find the eyeglass mounted 'aperture' (a la Merit) to clear the vision. It can be emulated by using a piece of black elec. tape with a pin hole stuck on your glasses 'where your eye actually looks through the lens' (inside/high usually). If you are using glasses for correction the optical center isnt where we look through when shooting a rifle. No see, NO wonder!
If you dont use correction ,well, we should all wear safety glasses when funnin' around, shouldnt we...........at least it gives a place to stick the tape.
So, put on whichever glasses, mount the rifle and sight down it to a target. Have a friend move a 'grease pencil' around on your sight eye lens until it is where you are looking through and mark the lens. That is where you want the pinhole to sit. Note that depending upon the stock this spot on your glasses can change around a bit. I have one that Im looking almost at the edge of the lens and the frame.....not good for clarity!
As to scopes, I have an old Weaver B-6 3/4" on one, slim & trim and matches the lines of the H&R so well, but mounts for the 3/4" and Weaver rail are hard to find nowadays. Otherwise I really like the old Weaver 2.5 to 3X, 1" tube as they have a 'straight objective' and small ocular bell. There are several newish scopes that do likewise and one (forget which?) sits nicely just forward of the hammer and would, without a doubt, be my choice if buying new.