Pretty encouraging first try, especially picking up some colour in M42 and capturing a meteor as well.
As has been said above forget about the infinity mark on your lens as most are not spot-on. I concur with the live view focus mode and aim for pinpoint stars.
Next time you have a crack at it try setting your Release Mode Dial to 'Mup' (Mirror Up) and if you aren't already doing so, use a remote shutter release and wait at least ten seconds after touching the camera/tripod before activating the shutter. This allows your set-up to stop vibrating.
Also have a play with Lightroom's 'De-Haze' filter which I find a handy PP tool for Astro shots.
As the shot is fairly clean you could also try pushing your ISO to ISO6400 and dropping your shutter speed to 15 seconds. The D750 is one of Nikon's best for low noise.Try different settings till you find the best combination.
And be warned, you are flirting with a photographic genre that can become an addiction.
RE your lens, have a look here .....
http://www.photozone.de/nikon_ff/551-nikkorafd2428ff
Happy shooting.