As you want to immerse yourself in one of the more demanding disciplines in our art/craft/hobby, I won't try to talk you out of getting more equipment until you have shot lots with what you have .
Does your style demand an ultrawide lens for your astro work? In that case, the fast Tokinas are the way to go, with the best being the 11-20/2.8.
If you don't need the larger field of view, the Sigma 18-35/1.8 is worth considering, because it is so sharp and contrasty and so fast.
This pair should cover your needs for ultrawide to normal focal lengths.
The next step in building a lens kit for mainly landscape and starscape work would be a short to medium telephoto, so something in the 50-100 mm range on DX. This is exactly what the Sigma 50-100/1.8 is, and again, it is the only one in it's class.
If you are into landscape, you will sooner or later want or even need a supertele zoom, either for wildlife or for that compressed look you get when you enlarge details that are far away. Here, any of the third-party 150-600 lenses or the Nikon 200-500 are good choices. The first that came out in this class is the Tamron in it's first generation. I, personally, didn't like how this lens draws and scrapped it from consideration when I tried all the available options last autumn. The reason I ended up with the Sigma sports version is that I found that lens easier to use while panning because it is so front heavy. The two Sigmas, the later Tamron and the Nikon are all very similar in optical quality and VR performance.
My ideal set of zooms for DX on a budget today would be:
Tokina 11-16/2.8 (cheaper) or 11-20/2.8(better)
Sigma 18-35/1.8
Sigma 50-100/1.8
Sigma 150-600 Contemporary (cheaper), Nikon 200-500 (better, but only 500 at the long end), Sigma 150-600 Sports (better, but heavy) or Tamron 150-600 G2 (better)
These all offer better quality and/or are faster than the competition in their price range. The only disadvantage is that the first three are DX lenses, so they won't work too well on an affordable FX camera.