1. PADI v. NAUI. While I prefer NAUI, there is a much wider spread between instructors than there is between the two agencies.
My advice: Start by reading the Sticky Threads at the top of this forum. There are things to look at and compare between class offerings but, IMHO, NAUI or PADI would be about the last on the list. If you want to ultimately do the super skilled thing down the road, I might suggest something like GUE-Fundies or some true tech training from tech agency.
First: Focus on a class taught by a great instructor. Look for more pool and class time. Look for a shop that also offers shop dives after you are certified. Look for a good ratio of staff to students. Location and schedule matter in place as large as LA. But be willing to drive for quality. If you plan to dive So Cal regularly, look for dive shops that have that vibe (rather than veryone goes to Cabo or Maui vibe).
Second: Finish the class and do a few dives. The evaluate.
2. Gear.
I would start simple: mask, fins, snorkel, booties. You goals: stay within your budget, get gear appropriate for local divings and get gear that fits you well! Because fit is so important, I would shop locally if at all possible.
The #1 criteria of masks: fit!. While I prefer some masks over others (I use
Atomic Aquatics Frameless Mask ), you will
hate any mask that fits poorly. It will always be flooding or it will hurt. No need for the best quality or any fancy gizmos. A like this advice:
Mask Fitting . Also, learn how to clean your mask so that it is less likelt to fog.
For a snorkel, avoid something really complex (there is one that is reall two in one -- and exhale and an inhale) and avoid the old J tube. I personally prefer a dry snorkel but some others don't. I love the Atomic (
Atomic Aquatics SV Series Snorkels ) but $50 for a snorkel?
Booties: I prefer a 7mm wetsuit booties with a very solid tread. Might be overkill on some dives but they are great when you need it. Again, fit is also crucial. An example of what I use:
Boots (the Pro Boot). I want something I feel comfortable walking over sharp rocks in while wearing full gear.
Fins: Lots of room for debate here. First rule: They must be open heeled and not full foot. Second rule: They must fit and not cause cramping. While wearing your dive booties. There are at least three major schools of thought on fins: old style Rocket or Jet fins; paddle fins; or split fins. And then there is the force fin crowd. Ask around. See if any dive shops have any you can try in their pools. For paddles you might look at something like Mares Quattros and for split something like the Apollo Bio Fins (I only name these two because I have used and enjoyed them).
3. More gear. The class may require to buy additional gear. If so, you have limited options. Otherwise, rent different gear. Try stuff at try-out days that some manufacturers run. Go to the big show in Long Beach each year. Borrow stuff from other divers. Don't buy more right away but learn about gear -- what you like and what you do not. What is a good value and what is not.