A decently rated zoom lens within reach of your budget is an
SMC Pentax-FA 100-300mm F4.7-5.8. KEH has a copy for
$109.
I don't own this lens, but considered purchasing it, when I got started some years ago. A surprise windfall of funds made other selections available to me; hence, why I never bought it. Like myself back then, it seems you're interested in exploring telephotography, and this lens could be a good fit for you.
Of course, I would always wish a surprise windfall of funds on anyone looking into photography.