You can start with most anything from the major brands (Canon, Nikon, Sony, Olympus, etc.), your main thing with portraits will be lenses and lighting. If you pick up an DSLR, I recommend picking up a 50mm f/1.8 lens, great for portraits, great quality, fast, and works well in low light. You can learn quite a bit from that lens. Lighting will come down to natural and artificial, the latter being flashes and strobes. External flashes will supply more adjustable light than what comes with the camera, they usually run off batteries or packs, great for portability. Strobe lighting kits are great for shooting and controlling the light, this what I use most of the time, these plug into a wall or you have to get a portable power supply for them:
If you go this route I highly recommend wireless triggers, basically a transmitter mounts on the camera and the receivers mount on the lights, without that you have to tether a sync cord from the camera to the lights. I have had good luck with the Alien Bees products, here is one to get started:
Paul C. Buff - The Beginner Bee Package
I use a pc running Win 7 64bit, 8gb of ram, old school quad-core processor with a few TB's of storage. It's old but it works with Photoshop CS6 just fine, I plan on upgrading after the 1st of the year.
I have a website:
www.elianthony.com have links for networking on my contact page.