Knowing how to light for portraiture - being aware of lighting styles and lighting ratios would tell you what you need to get started.
From that you would research what products are available.
The physical dimensions of the studio space need to be considered.
You will need at least 2 lights (key, fill) plus some lights for the background, but having 5 lights to light your subjects will give you more lighting options from the beginning (key, fill, accent/kicker, hair, rim).
Some pros prefer studio monolights, like what Profoto, and Elinchrom offer
Some prefer a head and power pack light system, like what Speedotron has.
As far as light modifiers some prefer to use umbrellas (Westcott), some use brollys (Photek), some use softboxes (Chimera), and many use all 3.
You will need to have a variety of sizes from the beginning. You use the smaller sizes for head shots and the bigger sizes as more of a person is included in the portrait or when more than 1 person is in the portrait.
You'll need some reflectors and some diffusion panels in a variety of sizes. Lastolite is a good brand.
You'll need a posing stool(s), a camera stand, gaffers tape, extension cords, yada, yada, yada. (Manfrotto, Foba, Arkay, make camera stands)
Light stands should go up at least 8 feet, be sturdily built and stable, but you'll want light stand weights anyway. I recommend Matthews brand light stands (C-stands) and boom arms for lights.