Hi -
Congrats on the new addition.
I started with other software but for under $100 you can't go wrong with Sony's Vegas Movie Studio.
You can download a fully functional, 30 day trial here:
http://www.sonycreativesoftware.com/download/step2.asp?DID=736
If you decide you like this stuff - it's a simple move (only requiring a couple hundred bucks) to move up to the full version of the product.
That said, you get an amazing amount of functionality in the Move Studio version so you would only have to upgrade if you decide you need advance, professional features. You can also download a 30 copy of Vegas+DVD on Sony's website if you'd like to play before deciding.
Good luck.
Bruce