I didn't have intake paperwork at my first visit, but I now work at a place that does have the client fill out papers before coming into the office. This is just speaking for our place, but brief answers to the questions are fine, being thoughtful and insightful is not necessary (although those qualities are of course always good!). We use the intake papers to identify areas the client may need help with, so really just flagging that something is an issue is enough, like "marital problems", "relationship issues", "abuse history", "depression", etc. You are right, your answers can serve to help guide the conversation at the first meeting.

There was good alignment. He presented to me at the first meeting like he is now. Very genuine, no bait and switch! I had an immediate very positive reaction. And also, an immediate connection. After just one session, I felt he would be able to help me. He gave me confidence he could handle this problem. (My previous therapist had not been like this.) I felt HOPE, which really helped my mood and outlook too. It turned out he was indeed able to help me with the problem I came to him with, and now we are on to other things.

Best of luck at your first appointment.