It looks as if you have it correctly decoded. My old rifle was serial number 1583XX with letters RM (Nov. 1965). Your carbine will be perfect for your kids. Sounds like you have a good scope suggestion, thats Leupold's best scope I.M.H.O. SWEET!
I thought they went to a 22 inch barrel for the standard cartridges in 1965? And 63-64 were the years with the 20 inchers?
Casey