I have one of those. It was given to me by my mother on my sixteenth birthday, fifty years ago. My advice on a scope and mounts, is a Center Point scope.
I believe Walmart sells them in a 3X9 or 6X14, They come with decent mounts, and you will definitely be able to get your cheek back on the rifle with them. They both have lighted reticles, and nice turrets, and the 6X14 has adjustable objective (very handy) and flip up lens covers. I have three of these, the most expensive was $69. For my money it's the best bang for the buck. Additionally there is a life of the scope guarantee from the maker. If I had to choose I'd go with the 6X14.
Here is the Walmart page with from reviews:
http://reviews.walmart.com/1336/10248654/centerpoint-4-16x40mm-scope-reviews/reviews.htm
When I decided to buy my first one I was skeptical, but I figured Walmart is good about returns. Two of mine are on .22LR rifles one is on a Marlin lever action that I have been testing .357 magnum reloads in. I have some expensive scopes on other rifles and they are great, but these do the job well, for what you pay.
I don't know if you have tried different makes of ammo in yours, of the ones I have tried, the rifle seems to do the best with the higher speed ammo. Mine is an OK shooter, I have re-crowned the muzzle, didn't help much. I'm going to keep testing ammo, to see if I can tighten up the groups. I keep it mostly for sentimental reasons, and I'm spoiled by a couple of my other rimfire rifles. Yours is in pretty nice shape. I have refinished the stock on mine with Tru-Oil, turned out real nice and was easy to do.