Hi Ariel -
Welcome to the board, and welcome to cycling!
While I do wear a sports bra, underpants are definitely not needed under bike shorts. Just try on enough shorts to find a pair with a comfortable chamois for you, and plan on washing your shorts after every wearing. Underpants are not necessary and an uncomfortable extra layer. My shorts of choice are Pearl Izumi Ultrasensors - but we're all different, and if you keep reading here you'll find that we all like different shorts.
On the sports bra side, good sources are the Team Estrogen site and Title 9. I've been wearing Champion bras lately though, and I usually get them directly from their web site.
--- Denise