Hello there and welcome to the forums. With the K-3 you picked a very nice piece of gear to step up from point and shoot.
Did you get a kit lens with it? Depending on its range you could try around with the different focal lengths to get a feel for what kind of prime would best suit your needs.
The 50mm 1.8 is, just as advertised, your typical portrait lens. And I think it's way worth its money. So if you're interested in that type of photography this might be the pick. It lets you take very nice close-ups or keep a bit of distance for full body shots (it is a mild tele). Some prefer to use 100mm or such for portraits, even, but you would need that much more space. Not a bad thing for kids, of course, as you get to stay out of the way.
I had to do some upper torso shots in more confined space recently and got the 35mm 2.4 for it, in addition to the 50mm. As I understand the 35mm is typical for for street photography, since it's roughly your normal field of view. I do think they complement each other quite nicely.
In hindsight the 40mm limited may have been the better choice for me, just one lens in the middle of those focal lengths, but it is more expensive, too.
For landscape an extreme-wide angle could be something to look into, but those are probably a tad out of your price range. I think the Tamron 10-24mm ain't too far off, being one of the cheapest options (not sure about primes though).
Oh... I'm still rather a newbie, too. Just some thoughts, they're not backed by too much experience!