Congrats on entering the 21st century! Now, read that little book in the glove compartment.
You will do a bit better overall with the engine oil a little bit 'under' and the tire inflations a bit 'over'. Don't be surprised if the engine oil appears overfilled though; a lot of them arrive that way. Just fix it.
Due to Toyota's cleverness it is basically impossible to drive the car 'wrong'. However, for best fuel economy you ought to read some of the fine posts in the internet groups, and see how much of that advice you can use.
Most important for a newborn is to take your eyes off the little TV screen and avoid other cars. Don't be the next one posting a picture of your new crashed baby; we have seen too many of those already.
Very likely driving Prius will be calming, and that might spread to other areas of your life. It wouldn't be the first time...
The technology of the synergy of the electric and gas engines is amazing. The constant transisitioning, working in tandem and shutting off and on is almost seamless. The first week or two I had my Prius, the slight shuddering as the engines transisitioned was somewhat of a concern and annoyance. However, I got used to it and rarely if ever think about it now.
Also, you may be surprised to find the Prius idling while stopped. It is normal for it to do so when warming up for the first minute in warmer weather and a few minutes in winter. Also, certain battery state of charge states will cause it to idle sometimes, even bucking a bit as it decides whether it wants to idle or not. But this is relatively rare.