Let's break it down as far as I can tell:
We want to make everything so that people think of old oil paintings (Rubens, John Singer Sargent, Michelangelo, etc.)
directional but soft
likely it's a softbox with a grid that's not too close to the model
strong shadows that define forms are super imprtant here, check out Rubens paintings if you want examples
He actually uses a painting here but you could use a classical painted/textured muslin here
here he uses props and hair/makeup that fits the theme and even the background
think greek and roman myths, gods and such
He creates an association to paintings instantly with that.
For simpler portraits you could use old timey clothes and hairstyle and makeup that's inspired by classical paintings. Props like jewlery must fit the theme too!
Photo gear and exposure:
pretty much evertything must be in focus, paintings from that time didn't have background blur!
Lens must get you sharp details (at least in the centre) but musn't have high contrast. For example old single coated lenses and old russian lenses, more character is better so keep the aperture open if you can. There are soft focus filters that can help with the effect but your milage may vary.
Shutter speed is not important because flash.
ISO is not very imprtant because it's not about pixel peeping.
I can't help you with that but you should propably research paintings you like and match those. The way the color of those old oil paintings aged is not obvious on first look but important because of the associations!