You’re making (or have made) a new human? That’s pretty incredible. I really get how full your heart feels right now.
In all my photography work, I chase light and emotion, and let the images fall out of that as they will. If you would really love a whole series of posed photos where everyone is looking at the camera and smiling, that's great, but I might not be the right photographer for you (although I can always try to include one of those in your session as I understand that grandma might love that photo the most).
I would describe my newborn photography as raw, and heart-centred and soft. My general approach to all my family photography is highly responsive to my clients and the way they live, so if you are generally loving and relaxed, or a bit more high energy and extroverted, then the photographs I make for you will reflect that.
This tiny new person will grow and change so quickly, you will never regret setting aside a few hours to sniff your baby (how good do they smell!) and create memories you can hold forever.
I really don't think that there is any one 'right age' for photo sessions; the perfect time to capture your newborn or young baby is always 'right now'. I sometimes hear parents (and other photographers) talking about photographs in the first two weeks, or waiting for babies to smile at the magical 6 week mark, but none of this is truly important. Although some of these days feel impossibly messy or hard or tiring when we are in them, when they are gone, we will miss them more than we know.