I got a plumber to do mine, when I already had gas into the house. Call your regular guy, he can steer you to the right party if he can’t do it himself.

The HVAC company and the plumber are both in the pipefitting business, but I think you should have someone whose judgement you trust have a look at your present setup, and listen to your plans for the future. Running a gas line isn’t rocket science, but of course the safety concerns leave no leeway for slipshod work.

I’d go with a plumber I trust.

And yes, at least in my state, you would need a permit.

Plumber who knows how to deal with gas lines.

A plumber, one who is qualified for installing gas water heaters.

Since you’re going to have a contractor do it, call a licensed plumber that you trust and ask if they can install it. If they can’t, they can recommend another contractor who can. Tell them that you want them to pull the permit, too, if it’s required.