The answer is yes, it is a good gun that is not necessarily cheap, but a good value.
I believe there are other options out there that may be better. The H&R single shots can be quite finicky to get to shoot right, so I would suggest a less expensive bolt action.
Since I don't know what your budget is, I would suggest a Stevens bolt action. Stevens is a subsidiary of Savage, and their rifles tend to be very accurate right out of the box.
Since you are talking just about a rifle, it sounds like you would also need a scope. If that is your intention, check out the Savage website and look at their package guns which include the scope as well.
The scopes are decent, but the rifles are excellent. You can always upgrade your scope at a later date.
As far as the length of pull, most of the rifles will fit you just fine looking at your height. You shouldn't need to do much of anything with the stock.