It takes a warm load in .38 Special to get a hollow point bullet to expand effectively, and it would be a shame to subject that old war horse to that kind of treatment. (Not that it won't take it for a while, but warm/hot loads definitely accelerate wear on a handgun).
So, I would consider the classic .38 wadcutter, over a powder charge just slightly better than what is, (or was), typically used for target shooting.
Use a fast burning powder, like Bullseye or 231, (yes, I know I am dating myself, old school powders are what I was using last time I loaded .38s, I use newer powders for my auto pistol loads, I promise).
Just work your way up closer to the max loads recommended by powder or bullet manufacturers.
Not a wonder bullet, but it will make a larger hole than more conventional style bullets, yet still penetrate well.
It is an accurate choice, with light recoil and flash, and its modest pressure levels should let you enjoy that gun for a long long time.