Lots of opinions about optimum scope for deer hunting. 4x is not bad at all, actually, but more modern scopes will be lighter, gather more light, and offer other advantages. A variable power scope is very useful, and 3 to 9 power is HUGELY popular. Just about any El Cheapo 3x9 is optically superior to the current scope. JMHO.
Unfortunately, putting a modern scope in the best, most useful position will require a lot more gunsmithing on your rifle. Basically, the rear sight will have to be milled off altogether, and the receiver bridge drilled and tapped for scope bases. This was fairly popular back when sporting rifles were expensive and gunsmithing time was cheap. Now, it makes no economic sense, but with heirlooms, that's not likely to be an issue.