The best Pentax lens for portrait photography is the new premium Pentax portrait lens — the DA* 55mm f/1.4.

http://www.pentaximaging.com/camera-lenses/smc_PENTAX_DA_Star_55mm_F1.4_SDM/

http://www.bhphotovideo.com/c/product/594340-USA/Pentax_21790_55mm_f_1_4_DA_SDM.html

The DA* 55mm f/1.4 replaces the old 85mm f/1.4 portrait lens. 55mm on Pentax digital cameras is about the same field of view as 85mm on film. The focal length multiplier for the K20D is 1.5385. 55mm x 1.5385 = 84.6mm, and focal lengths on most lenses are rounded.

The FA 50mm f/1.4 is also a fine choice for portraits, and I use it for that. The bokeh (blur of out-of-focus areas) is beautiful, though probably not up to the 55/1.4.

The new "II" version of the 18-55 kit lens is generally excellent for a kit lens and a great value, and not a bad lens to have for general shooting when you want to travel light. But it won't allow throwing the background as much out of focus (f/5.6 at 55mm compared to f/1.4), and it's bokeh won't be as pretty.

If you want a medium zoom to double as a portrait lens, I would look at:

— Pentax DA* 16-50mm f/2.8
— Tamron 17-50mm f/2.8
— Sigma 18-50mm f/2.8
— Sigma 24-70mm f/2.8
— Sigma 24-60mm f/2.8

However, don't expect the best bokeh from any such zoom. I have the highly regarded Tamron 17-50/2.8, and I like it very much for a medium take-everywhere zoom, though I had to send it to Tamron for warranty service (it had a bad case of front-focus). But on difficult bokeh such as trees and bushes, it doesn't look as pretty as the 50/1.4. It's fine with easier bokeh such as large, rounded shapes.

Good luck and have fun!

Greg
References :

I have the earlier version of the lens and it is quite good in the center, but soft around the edges- poor for landscape but good for portraits.

However I recently purchased the Pentax DA* 50-135mm f2.8 SDM lens and one of the intended uses is for portraits.

With the Pentax crop factor of 1.5 this makes the lens equivalent to a 70-200 mm zoom on film or full frame digital SLRs.

The * indicates it is one of Pentax's premium quality lenses.
References :
http://www.aviewfinderdarkly.com

Since I have a bias against variable aperture zooms, I think you should look at the Tamron AF70-200mm f2.8 Di LD (IF) and the SMC Pentax DA Star 16-50mm f2.8 ED AL (IF) SDM. This would be, in my opinion, an excellent 3 lens kit.

Also, keep in mind that every Pentax K-mount lens made since 1975 can be used on your K20D. Yes, there are some limitations with the older manual focus lenses but they can be used.
References :
37+ years of learning about and enjoying photography.

The 50mm on a 35mm camera is the one which is closest to the human eye in terms of field of view.

Anything under 50mm is liable to "distort" portraits especially when you are close to the subject.

An 85mm would give you good head shots and you would be able to get full length shots in easy enough by moving a little.
Get the fastest lens you can (lowest f number) so that you are able to throw the background out of focus.
a
References :

105mm 2.8 prime lens.

And that's the answer for a reason. You'll get great results with a lens like that. Short lenses introduce distortion. See this video, you'll get some ideas for what you need.
References :
http://www.layersmagazine.com/photographing-portraits-with-zoom-lenses.html