Treat this the same way you might go over a lease for office space. Let them make the initial offer (they have much better data about market rate and what they are willing to pay, you don't and may box yourself into a lowball position). Then take some time to figure out if it works, and take the comp discussion offline.
Keep the negotiation about compensation in writing. There are a million ways for an experienced negotiator to manipulate you in a live conversation. Break things down (salary, PTO, equity, 401k match, telework, other hard benefits), and figure out where they'll budge. And remember, it's not about being greedy, you'll be locking in your pay for 1-2 years, and you're doing your job of negotiating a good deal for you and your family. If someone doesn't respect that, that's a big red flag right there.