At some point the conversation moves offline. That step is normal and necessary. A few plain precautions make it uneventful.
Somewhere public, and your choice
A café, mid-morning, in a place you know. Not their home, not yours, not a car. If the suggestion is somewhere private, the answer is no, and how that no is received tells you something worth knowing.
Tell someone
A friend gets the name, the place, the time, and a message when you leave. This costs nothing and changes what a bad situation looks like.
What not to bring yet
Your home address, your workplace, your surname if you have not shared it, and documents. There is no first meeting that requires any of those. Anyone who needs them at this stage is moving faster than the situation warrants.
What the meeting is for
Not to decide. To find out whether the person in front of you matches the person you have been talking to, and whether you can imagine a difficult conversation with them going well. That second one matters more than it sounds: you are assessing a future negotiating partner, not a date.
Afterwards
Give it a few days before responding to anything significant. The people who report regretting this process almost never regret going slowly.