With your budget, I would get the HD 55-300 (399 on Amazon) for wildlife, and a Tokina 19-35 f/3.5-4.5 (110 used at KEH) for landscapes.
If you don't mind buying both lenses used, KEH has the SMC 55-300 (previous version, same optically, slightly different coatings) for under 300 and the Pentax DA 16-45mm for 245. Look up the 16-45 on flickr, it is a very nice lens for landscape and nature pictures!
There is also a DA L version of the 55-300 (plastic mount, no quick shift) that sells used for about 170. That would free up more money for the landscape lens. But I personally didn't want that lens even though I could probably have bought it, because I was nervous about getting a lens this long with a plastic mount. But if you think that won't be an issue, the DA L is a great value! Optically the same as the SMC DA 55-300.
I also have a K20D. In a similar situation recently - wanted a lens for kids sports, and one for landscapes, but with a budget of only less than 300, I ended up with the aforementioned Tokina, plus a Tamron 70-300mm f/4-5.6. The Pentax 55-300 is a better lens than the Tamron I got, but I'll have to make it work for now. Now the Tokina I got is very sharp stopped down and has great colors, so I'm pretty happy with it. I don't really need the superwide side of things (like a 10-20 or 12-24), which would be out of my budget anyway. So I am happy with what I have now, and all my lenses are compatible with my film Pentax camera, with the exception of the kit lens 18-55 which I don't use anymore.
Last edited by ChristianRock; 02-25-2014 at 11:44 AM.