I am a high functioning Aspie engaged to a neurotypical... probably because he might secretly have AS as well (I can see some of my Aspie traits in him, and we're socially awkward to list a few things. lol).
I was about to hit submit before I started writing this part above the paragraph below but as soon as I reread your post, I have more to say since you're still in "early phase" with this guy: Don't worry about eye contact with him too much since it's something that's out of the comfort zones for a lot of Autistic people/ Aspies. It's almost as intimidating as talking on the phone in my opinion. Avoid using sarcasm in conversations unless he initiates it. Some of us take everything literally, and we speak/think literally because of it. I definitely take almost everything literally, but in recent years I have embraced the art of applying sarcasm in social settings thanks to lots of help from my fiance and the medical drama show House.
NOW, I know you've only just had your first date with this guy, but since I am in a committed relationship with a neurotypical I feel that I might as well bring up the "if you plan on getting serious" advice... just in case, ya know?:
As you get to know this person more, you'll learn more about what makes him awesome, and what you see as his "flaws" (I could go on for days with personal examples. Too many to pick just one or two). I have been with my guy for almost 7 years, beginning when we were just a few months from turning 19... so that gives you an idea of how much I have changed for the better in just a little under a decade thanks to him. I say this because if you stay with this guy, my advice could serve as an advantage as long as you have patience. The Spectrum can be a different language at times, but if you nudge us just right we'll listen and do something about "our flaws". Sometimes I learned the hard way (and I totally hated it until the new concepts grew on me, which is still happening to this day. I'm always growing up.), and some things were honestly maturity-related, since I am now 25 and "older and wiser". He cares, so I care. Makes sense, right? Don't be brutally honest to any degree unless you feel it could be productive and helpful because meltdowns suck, and I almost made it 6 months without one. Had my first one since September 22nd last wednesday. There are so many things that can trigger meltdowns that you would least expect, and harsh criticism is one of the biggest triggers for me at least. It's inevitable for sure, but there are lighter ways to be brutally honest with someone, like talking to them in privately instead of in front of a ton of people in a public setting and attempting to phrase what you want to say "gently".
Good luck, and if you need anything else, you can message me. Happy you came here to ask us!