Funny that there was a similar discussion in my office a few days ago involving one of my co-workers and an intern on this subject.
To sum it up, the good thing with starting in portrait shots (as opposed to landscape) is that you have more factors that you can control (it's easier to arrange a photo session with your subject as opposed to waiting for Mother Nature to stop the rain at the National Park which is 8-hour drive away).
Like what others said, primes are great for portraits since you get faster lens at an affordable price, and there's no need to worry about using a zoom lens to cover places you cannot enter on foot.
However, u'll probably need to invest in gears such as reflectors, strobe diffusers, strobe cable, wireless trigger, multiple strobes, etc. (The good news is that you can buy several of these items for the same price of a Gitzo tripod).
It's also nice to have another friend along, who can hold the reflector for you when you take shots of the subject.
Lighting system? You can always start out with outdoor lighting if ur not ready to invest in a studio setup.