Hi Mike,
I'm a fellow newbie (25 dives). Here's my $0.02
The "what to buy" question is kind of overwhelming. Information is available from many sources -- scuba mags, chat boards, fellow divers, etc., etc.
One critera I found useful to help narrow down my choices is to decide which of your area dive shops you feel "comfortable" dealing with -- they seem helpful and knowledgable, etc. Then evaluate what brands they carry. This may help guide your choices to some extent.
I am currently in the market for a new regulator and computer. Using various Non-dive shop sources (net, scuba mags, friends, etc.), I narrowed my choice downs to 3 or 4 regs/computers. I then went to the 3-4 dive shops that I like in my area to see what brands they offer. Although I would never recommend having a dive shop be the only driver for equipment choices, service after the sale is important to me, especially for life sustaining equipment like regulators. I feel more comfortable buying equipment from a shop I have a relationship with and know something about vs. driving far away just to get a better deal or specific brand. I also want to buy both the reg and the computer from the same shop in the hopes of negotiating a better deal (buying all from one shop typically results in better savings).
All that being said, here are a few equipment recs (GENERAL recommendations, since I don't know anything about where or how you plan to dive):
Regs -- I narrowed my choices to Atomic and Scubapro, but these are pricey options. I've heard many good things about Oceanic -- the Delta III is one of the best buys out there for the $$$.
Computers -- Suunto...conservative, easy to use computers with Nitrox capabilty. Better to buy something that is Nitrox capable now vs. having to buy another one later.
Good luck.