If you really want to explore the different types of portrait photography, here’s what I’d suggest: 

A reflex camera

A lens with a wide aperture (2.8f ideally) 

A tripod

A flash and reflector 

A gray card 

A model

What lens to chose 

Different lenses are going to give you different effects, for example, a longer focal length will help flatten a face, which is sometimes preferable. However, with a longer lens (think 200) you’ll have to compensate for stability and you’ll have to shoot with a longer shutter speed. (If you are just beginning photography and this doesn’t make a lot of sense, check out this article about the basics of shooting in manual and then come back!) 

I personally love shooting with my fixed 50mm 1.4f lens. The aperture can open so wide that it allows me to shoot beautiful photos even in low lighting. Ideally, you want a lens that can open as wide as 2.8f so that the subject’s full face in focus, while creating a bokeh effect.

To be contd.