Portrait work has been strictly a hobby for me. I've built and purchased quite a bit of gear over the years, but this is my basic kit:
4) Yongnuo YN-460ii, generally under $50 each at Amazon.
16) Powerex AA 2700mAh NiMH batteries for above
2) Cowboy Studio NPT-04 wireless hot shoe trigger (transmitter and receiver) for $23 per set at Amazon. These are so cheap, I bought a second set for backup, but sometime use it with a backdrop flash that might be hidden from the key or fill lights.
3) SP and Photoflex umbrella multi-brackets at $18-30 each.
2) Interfit Tri Shoe adapter ($13 each at BHPhoto.com)
3) 7' stands by Photoflex and Bogen, but I'd recommend looking at cheaper options, maybe Wescott.
2) Photoflex 45" white satin umbrella (model RUD45) at $23 each. I have collected many 45" Photoflex umbrellas including white with black backing and silver with black backing, but I like these white satin the best. I can shoot through them or bounce off them and don't worry about not having a black backing.
2) Photoflex 60" white w/removable black backing umbrella (model PHU60C) at $45 each. I generally use just one for a key flash, but like the flexibility of having two.
1) Impact 5' x 7' collapsible white/black background at $70. This is a recent purchase and has been great to work with for 1-2 people shots (mostly 1). I generally make my own backdrops by tie-dying muslin or king size flat bed sheets and making the stand out of 1 1/2" ABS pipe. But, impulsive shots of my kids or portraits on the go, this has worked out great.
I have also made a few 39"x72" PVC stands for white/black Photoflex fabric to be used as reflectors. But, I save these for more indulgent acts of creativity.