Full frame or APS-C? [IMAGE'S LINK: https://flic.kr/p/kRyn6x]DPP_0794
I use a 35 F2 IS often. You can frame the galactic core nicely even on APS-C with this focal length. F2 is helpful, and it handles coma nicely (not perfect though, but nice). I also use this as my "wide" every day prime on full frame.
Here's the 35mm F2 IS on an APS-C for the galactic core:
by Martin Wise
, on Flickr
I like it a bit wider, room to crop and handle bad coma. This is uncropped, you can see the coma at the edges (look for football shaped stars). You can stop down to help correct this, but F2 gives you a lot of light to work with.
Ideally, I'd say the Rokinon 24mm F1.4, but you want AF, so that rules that out.
Honestly, I'd suggest you get whatever lens you like for every day, and simply get a $300 tracker so that you can expose for 2~4 minutes at F2.8 and F4.0 without worry around ISO 1600 or so. Much better return for your money.