Three other suggestions for lenses in the 70-200 range. Though the Vivitar Series I lenses are widely recognized as lenses to look for, this also makes them less likely to be found at a reasonable price. . . but there are other very good models out there.
The Pentax A 70-210 f4 is a very good one, and is usually very easily available. It's sharp from wide open and is manual focus but has the electrical contacts to allow Auto Exposure. Prices can range from @ $65-150 USD, and I would consider some of the lower priced examples to be one of the best bang for the buck zooms for the K-mount. I have one of these, and will never sell it.
The Pentax F 70-210 f4-5.6 allows both Auto Focus and Auto Exposure. Since it's not a constant aperture zoom, it's a little slower at the long end, but this is one of the better performing consumer zooms in this range from any mfg. I've had one of these, but the zoom helicoid broke, and since I have a very good DA 50-200/4-5.6, I never replaced it.
The Tamron 70-210 f 3.5 (mod 19 AH) has a reputation of being one of the best in this range. It's largely unheralded, so they can be obtained at good prices, but you'd also need to get an Adaptall 2 PK/A adapter to fit it to your K20. These (the adapters) have become relatively rare, and command some pretty high prices (compared to other mounts), but having one opens up quite a few great lenses in the Adaptall 2 series to use with Pentax cameras. All of the Adaptall 2 lenses are MF with AE (with the PK/A adapter). According to the author of the Adaptall 2 site, this one blows the Viv Ser 1 lenses away. . .
I think that you've made a good choice of bodies, and am looking forward to seeing some pics once you've gotten things sorted out. . .