Hi Sarah,
I've been hosting for a few years and increasingly rely on my intuition. It's served me quite well. I've had many wonderful guests, and also a few which weren't horrible although did confirm my intuition.
With that said, I also use my head, and also prefer guests who have reviews and some AirBnb experience.
I take as a good sign they mention their 9-year old in advance.
In general I wouldn't worry about a mention of discount. I've seen the request for a discount most often from those who haven't used AirBnb, and don't notice that I have already discounted the price from the daily/nightly rate. Most important suggestion I'd have around that is to be certain to keep the finances all through AirBnb in case of future dispute.
Also, although you're undoubtedly eager to host your first guest, it's also wonderful to have delightful guests. Would it harm to wait a bit for someone who fits a bit better?
Enjoy,
Dan