. . . and welcome to the forum!
I use TCs extensively, but only with lenses at least a stop faster than your 18-250 (f 4.5 or faster). The advice given by Dave and Th is good, especially concerning max aperture (lens speed).
The K20 does well at high ISO, so by bumping this up, you can compensate for the speed loss as far as exposure goes, but you'd likely be losing at least some AF capability, even with a 1.4x TC (your lens would have a max aperture of about f8.8 at the long end). The viewfinder image would also be a bit dark to focus accurately manually, so you'd only be able to use it practically in pretty bright light.
Another factor you might consider is that wide range zooms (over about 3x range), though amazing in their IQ (Image Quality) nowadays, suffer a bit more from design compromises to get that range, so aren't always the best candidates for TC use. The general rule is -- the better the lens, the less IQ is degraded by a good TC. TCs will always compromise IQ, but this effect is negligible or at least acceptable with high-end lenses.
Luckily, the K20 has a lot of resolution, so cropping is probably your best bet -- or you can always "zoom with your feet" -- get closer. . .:-)
BTW -- I don't use or recommend any of the 2x TCs with the possible exception of the Vivitar 2x Macro Focusing TC for its special close focusing ability.
The best TCs optically for K-mount lenses are generally conceded to be the Pentax models, but they are Manual Focus only so far (there is one exception, the F 1.7x AFA which allows sometimes limited AF with any mount comaptible lens about f4.5 or faster). There is a new SDM TC that's been tentatively announced that will have AF capability, but there's little info available, other than it's going to be a 1.4x, and both SDM and screw drive compatible, and will probably be pretty expensive.
Tamron (generally accepted as a rebadged Kenkos) markets AF 1.4x and 2x TCs that are not that expensive (a bit over $100 USD for the 1.4x), but very good optically. The Kenkos are listed as 1.5x and 2x respectively.
Sigma makes 1.4x and 2x TCs their EX APO line, but there can be compatibility problems with a lot of lenses because their design requires use of a main lens that has a recessed rear element. The 1.4x currently sells for @200 USD.
Congrats on your new camera -- be sure to post some pics -- we're always interested in the wide range of subjects that our members here like to shoot.