I agree completely with the sense of calm that comes with finding out more about baby. I've had monthly doctor visits, maternal serum blood tests twice, and multiple HCG checks in early pregnancy, in addition to an early ultrasound at around 8 weeks and one coming up at 21 weeks (Thursday).
I can say with confidence that I'll always choose to do all of things in future pregnancies that I have done in this one (except maybe the first ultrasound, but that was only because my first pregnancy ended in early miscarriage). I find myself hearing about all these terrible worst case scenarios and worrying about them, but when I get news like "you're chances of having a Downs baby are the same as a 15 year old", it buys me a lot of peace and I get to enjoy my pregnancy for a while.
I'm really looking forward to the upcoming ultrasound for the same reasons that you listed, Jess. I know that once I know the sex and get to see that things look okay in there, I'll feel so much happier and more bonded to baby. Every new thing I learn makes me feel a little closer to him/her.
Also, I am now able to interact with baby via the poking game. I poke in one spot and keep my fingers gently poking in until baby kicks them, then I move to a different part of my belly to poke and baby shifts over to kick/punch there too. It's really fun and feels great to be able to have baby interact with us