hey Goro,
First, congratulation!
For your question, go with a smallest DSLR. I used to have a Canon DSLR camera (from Costco). Once your new born starts walking, you need a quickest reload camera to capture the right moment. DSLR provided that nicely. I used the DSLR for few years and got few good photos of them at 1st B-day or such. As I see newer point-n-shoot cameras advanced, I wanted it since carrying the DSLR camera for everywhere on top of all the baby stuff was burden. The point-n-shoot camera I got has all the nice features like upload photos thru Wifi, bigger screen, and all that but... quality of photo is not comparable. Since then, I don't have much good photos of my kids. Nowaday, I usually take photos with my phone or GoPro. but I wish I have a DSLR camera for many kids events.
hmm... I better get one before my daughter's ballet recital coming soon too.