Welcome, and congratulations on your K-3! It's possible to achieve high magnification at high quality for pretty low cost. If that sounds too good to be true, it comes at the cost of convenience and versatility. But it's well worth exploring this route, especially given your budget.
I would start with a lens you can use for normal photography as well as for macro. Depending on what magnification range you want, simplest would be a fully-manual macro lens, such as the Pentax-M 50/4. These can be had for under US$100. However, this lens only goes to 1:2 magnification, that is, half life size on the sensor. Put another way, at 1:2 you would fill the frame with a subject about 2 inches on the long side. To get to 1:1 with that lens, you could add 50mm of extension, or you could reverse it (with a reversing ring).
Another way to go would be a non-macro lens, plus extension and/or reversal. A 28mm manual prime will get you very high magnification if you reverse it, particularly if you add some extension. Or you could try a 50mm non-macro prime. The Pentax-M 50/1.7 is a great lens, cheap, and works really well reversed.
Lots of options for you, even within your budget, so best to start by thinking about what subjects interest you most, and what shooting situations you expect.
And be sure to read this:
https://www.pentaxforums.com/forums/54-pentax-lens-articles/152336-cheap-macr...lose-work.html