I was asked once: If you were to go on a dive trip and could only take a piece or two of your gear, what would it be? My answer, in order of importance to me, is:
Mask first! The annoyance of a poorly fitting mask is very distracting. Constant leaks can turn the best dive into a struggle, taking time away from enjoying the beauty of the dive.
Regulator/Computer... I have a custom mouthpiece for my regulator. It is worth every penny to me. I don't feel myself clamping down on it for an hour at a time. It locks into place comfortably. I would not want to swap out my mouthpiece each time I wanted to dive because different regulators attach the mouth piece differently. Besides, I'm lazy and its easier to simply bring my own. My computer is configured exactly as I want it so I don't have to stop and interpret what I see. Besides, it helps me maintain my electronic log book, which is more comprehensive than my paper log book.
Those are my "must have" items. Fins, c-card and paper logbook, and dive light are serious wants, but if I had to dive without mine, I could get by. Everything else can be rented if I HAD to.
Expect to pay between $500 and $1,000 to become certified in Northern California. That will get you books, lessons, mask, snorkel, fins, gas to and from Monterey, dinner, and various rental stuff.