For landscape, I like to use ultra wide angle lenses. I have the samyang 14mm F/2.8. Some (including me) love this lens and others have had bad copies or just didnt like it. Also, if I remember correctly, the sigma 8-16 is not designed for full frame sensors, so using it on the 5d mark iii will vignette or possibly damage the mirror.
Almost all of my lenses are primes, most of which fall into the 24-70 range, so unless you are looking into primes, I wont be of much help.
In terms of astrophotography, I am not sure what you are trying to achieve, but those pictures you see on the internet are not easy to take. Most are taken with cameras with an infrared modified sensor mounted on a star tracker to eliminate star trails. If you get really into astrophotography, I have read about people using refractor telescopes with built in star trackers to achieve good photos at 2000-3000mm focal length.
If you do use something like an astrotrac, I have heard that results vary with lenses over 400mm. Something to keep in mind when looking for lenses in the future.