Full frame is, IMHO, the only way to go.
Firstly for the extra real estate a Full Frame offers over a crop sensor, and secondly it's bigger pixels have
better light gathering ability, and that is what astro photography is all about.
Have a look here for a comparison of sensor sizes...
https://www.bhphotovideo.com/explora...ng-crop-factor
The two cameras I'd suggest looking at would be the Nikon D600/D610 and the Canon 6D. Both can be found in lightly used condition and with low shutter counts (< 10K) for around the $1200 mark. Ryda.com and their eBay store NoFrills often have factory refurbished offerings with 12 months manufacturer warranty.
Look here for a comparison on them ...
http://www.digicamdb.com/compare/can...vs-nikon_d610/
Don't be seduced by the low prices of the Gray Market offerings as they often have dubious heritage and warranty.
I second Greg Bradley's suggestion re the Samyang 14mm f2.8 as I have one and rate it quite highly.
Good luck in your deliberations.
PS: And yes, a stable tripod, quality ball-head and a remote release are mandatory.