Nx300- how to improve low light performance?

1600-3200 ISO will show noise reduction and/or grain and artifacts on any camera, to varying degrees. How much depends on settings and of course the camera.

My experience with the NX300 is nil as yet, but I've owned an NX200 and NX100. Both turned in very good low light, high ISO results with a modicum of post processing in Lightroom. The chroma noise is easily drawn out with little to no visible loss of readable detail, and I for one have no issue with a bit of luma grain in my shots. Unless you're needing to view a small cropped area of your image at 100%, it shouldn't really matter.

That said, you're using a good but non-stabilized lens and trying to take images of moving subjects indoors with low lighting. Without buying a lens in the f2.0 aperture range or faster, you're going to need to boost ISO and learn some post processing techniques via RAW. There are some tips for shooting moving subjects here that may help. One big thing is to learn how to hold your camera so that it's better braced against you, and another is getting good at tracking your subject and anticipating movement.

I for one have no qualms with shooting cameras like the NX series, my 60D, A57 etc. up to 3200 as long as I don't mind spending a few minutes with each shot in LR. I'm not entirely sure how well the 300 handles JPEG but I know the 100 and 200 were quite poor when it came to higher ISO noise handling. Even my A57 was only so-so at this... Best I've used would be the X100 (in terms of straight unedited JPEG at high ISO) but there you have a whole other set of compromises and such - not the least of which being a fixed lens.

I'd suggest the 30mm f2, as it's fairly bright and not too close (though not really wide)... And there's always my favorite solution, tracking down a good price on a vintage prime like the Pentax SMC Super Takumar f1.4 50mm and get a Pentax K adapter for about 12 bucks. It'd be manual focus, but AF in dim light can be spotty anyway, and with a vintage bright prime you'd be able to take pretty fast shutter at an ISO range more like 400-800. Stop it down to f1.8 and those Super Taks are pretty sharp. That, and you'd also get some sweet artsy bokeh and flare around lights and such at night with the aperture opened up.

This is a Pentax 50mm 1.4 I found just last month at a camera swap meet locally for a mere 20 bucks. A cheap M42 adapter and it works just fine, and looks quite cool on the camera. KEEP IN MIND that any lens with a big aperture of f2.0 or greater shot wide open in this way will make for paper-thin plane of focus, so it will be hard to keep moving children in that field... So you're back to either investing in a decent flash with a diffuser or turning up the lighting