nikon – Lens for astrophotography / landscape on a D5500

I just started in photography this year and I am looking to buy my first lens.

I am mainly focused on astrophotography (that is, on the images of the night sky, not through a telescope) and on landscape photography.

I got a Nikon D5500 with the included lens (18-55mm VR) but I am divided between some very good options, both the Rokinon 16MAF-N 16mm f / 2.0 Y Rokinon 10mm F2.8 ED AS NCS CS It seems that they are the main contenders (price to performance wise). checking online the first one seems to be the best choice for astrological photography because of the amount of light it can gather, but the ultra wide FOV of the second seems better for the landscape, am I right? And if so, is ultra wide really good for landscapes?
Would it really be worth it to pay extra for a Tokina 11-16 f / 2.8 PRO DX II To be able to put filters in the lens?

Finally, if you know of any better option within a $ 400 budget, let me know!

Thanks in advance for your help!