nikon – Lens for astrophotography / landscape in a D5500

I just started shooting this year and I'm looking to buy my first lens.

I am mainly focused on astrophotography (images of the night sky and not telescope) and landscape photography.

I had a Nikon D5500 with the included lens (18-55mm VR) but I am torn between very nice options, both Rokinon 16MAF-N 16mm f / 2.0 and Rokinon 10mm F2.8 ED NCS CS seem to be the best candidates (price to performance wise). to check online the first seems to be the best option for astrophotography because of the amount of light that it can capture, but the ultra-wide field of view of the second seems better for the landscape, is it? what do I understand? And if so, is the ultra-wide format really good for landscapes?
Would it really be worth paying extra for a Tokina 11-16 f / 2.8 PRO DX II to be able to put filters on the lens?

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

Thank you in advance for your help!