What's your budget first off?
I'm a Canon user, so I'm definitely biased towards them. And I'll be talking about their entry level DSLRs
Lower end of price spectrum I'd suggest a
Canon EOS Digital Rebel XS w/ 18 - 55mm kit. This is a crop sensor body that's pretty cheap and quite good, then kit lens is decent. However I'd suggest putting money into a
50mm f/1.8 lens as well, this is an amazing lens for the price and is probably the best lens to learn on.
If you've got a bit more money to spend look into a
Canon EOS Digital Rebel T2i with 18 - 55mm kit. This a better body than the XS though is still a crop sensor, but with better ISO and HD Video.
Really though, look at those two bodies choose one and invest in glass (lenses), good glass will make a much larger difference to your quality of photos than a higher end body will do. Basically you'll need high end glass for a high end body, so if you build up your high end glass collection you'll be ready for when you need a high end body.
That being said, this is my dream camera, a
Canon EOS 5D Mk II, it makes Canon's cheapest full frame camera and in my opinion the best or second best camera on the market at the time.
Also I currently have a Canon EOS 10D which is discontinued as of this time, and it could be argued that new Rebels are better than my current camera, however I haven't amassed enough cash or a good selection of lenses to justify upgrading to a 5D Mk II, but that'll be the next camera I buy.
EDIT: Didn't catch the first time through that you're interested in portraiture, in that case definitely still go with one of those two bodies, but definitely and I mean definitely get the 50mm f/1.8 and probably even the 85mm f/1.8 if you have the money for it. But those two lenses are amazing for portraiture.
Anyways, any questions feel free to PM me or anything and I'll be glad to help. Especially with learning the basics behind Aperture/Shutter Speed/ISO and how that relates to exposure and depth of field. =)