GHolly, please understand that any K-mount lens will fit on both the Kx and the K1. However, a couple of the most recent lenses (DA 55-300 PLM and DFA* 50mm f/1.4) are KAF4 mount lenses and will not
autofocus stop down (thanks Adam; dumb error on my part) on anything older than 2013, since the cameras lack the necessary electrical connections.
But more to the point, if you can mount a lens on the K1, it does not mean that the image will fully cover the larger full-frame sensor. By default, the K1 will crop to APS-C size (though this can be disabled), so any DA lens can certainly work on the K1, but it will not take advantage of the full sensor. There are counterexamples, e.g. the DA 40 Limited and DA 70 Limited, which do a pretty good job of covering the full frame sensor.
If you want to get a modern not-too-expensive walk around zoom, be aware that the DA 18-135 and DA 16-85 will be wonderful on your Kx, but won't cover the full sensor of the K1. However, the DFA 28-105 will do both, and provides a useful focal length range on both formats. If you want something wider, options are limited at present (the DFA 24-70 is expensive and heavy). Some of the older (discontinued) FA zooms may be of interest (20-35 or 24-90), if you can find them second hand. Or the old Tokina 20-35.
Last edited by Paul the Sunman; 12-28-2018 at 04:53 AM.