I recommend you buy Cressi Clio fins in yellow before your first ocean class.
These fins are made of tough plastic and will last a lifetime.
They are short enough to fit in a carry-on bag so they can travel with you anywhere.
High visibility yellow helps your buddy see you in our sometimes low-visibility conditions.
Even if you order a pair of long carbon fins later, you will never regret owning these. Don't worry that they are plastic - your fins will never be the thing holding back your freediving (at least until you start breaking national records!). I have worn these in competition and my instructor trainer, world class freediver Johnny Sunnex, has done freedives with these in the 80s. They are plenty powerful.
You can get these on Amazon Prime for about $30.
The wetsuit is the priciest piece of your freediving kit. For your first class I recommend renting a wetsuit from Bamboo Reef Monterey or one of the many other dive shops nearby for your first ocean class. They rent good suits for freediving for about $30.
If you are ready to buy a wetsuit, I recommend ordering one custom from Polo Sub in Italy. I have ordered several of these over the years, and they have lasted me years of near-weekly freediving on our rocky shores, as well as costing less than most off-the-rack wetsuits.
What type? The most basic type, "Smoothskin Open Cell" in black, is currently $268 (at time of writing, with EURUSD at 1.00), which is incredibly affordable. For comparison, a domestic Mako wetsuit, which is not custom made, costs $337. You can increase the price by getting "Forza Tre" or "Combined", which are both stronger than Smoothskin, or by adding a cool camouflage design.
What thickness? I recommend 8mm. People will tell you this is too thick, but it will get less warm over time, so this ensures longevity. Also, I just think there is no such thing as being "too warm" in our water. If you are really too warm, unfasten the top from the bottom, or take off your hood, and you will cool off nicely :) If you know beyond a doubt that you are a very warm person in the water (perhaps because you have built up brown fat by swimming in the Bay), 7mm or 6mm is ok.
Why custom? Custom fits better, so it is warmer. If your body is a different shape to the standard used by off-the-rack wetsuit makers, you will be a lot warmer and more comfortable in one that is custom made.
What to avoid? Avoid getting a wetsuit less than 7mm thick, or that is old and stretched out, or that doesn't fit you well.
Other brands to check out Elios and Bestdive also both do warm custom wetsuits.
I recommend you buy the "Fins & Foam" mask from me for your first ocean class.
It is really important to get a mask that fits your face. The Fins and Foam mask fits both Asian and European faces well (unlike a lot of masks which are designed for Italians :), and has worked for hundreds of Fins and Foam Freediving students in the past.
I order them wholesale then sell them to you at the same price I paid for them. You won't find a mask of this quality elsewhere for even close to this price. It mimics the most popular mask in deep freediving, the Aqualung Sphera, which retails for $79 (https://tinyurl.com/aqualung-sphera).
If you want to buy a different mask, that's fine, as long as you try it on in the store. Don't just order a mask off the internet, because many masks won't fit your face well, and having a mask that leaks will really make it hard to enjoy your time in the ocean.
A knife is totally optional unless you want to forage. But it can still be nice to have for safety (fishing lines, etc) and convenience (cutting ropes).
If you are ready to buy a knife, I recommend the Mako Kona knife (Standard Blade, not XTra Long Blade). The shortness of the standard blade makes it more stable, and the serrated edge really cuts. It gets rusty over years in the water but still works. Get the Marseilles-style straps because they are more secure in kelp forests.
I recommend wearing the knife on your inner calf because it is more secure in kelp forests, and this is the only place you can see it when wearing a mask & thick wetsuit, to visually verify that you have returned it securely to its scabbard.
I recommend you buy a "Marseilles style" weight belt from Hammerhead, Mako, Pelengas or others.
These cost $30-40 on Amazon. https://www.amazon.com/Hammerhead-Spearguns-Marseille-Weight-Belt/dp/B01MAV26CC
"Marseilles style" means it comes with a buckle, and the belt is slightly ribbed.
The buckle means the belt stays on reliably, while still easy to release quickly when needed.
The ribbing makes your weights less likely to slide off the end when you unbuckle it.
Get fluoro yellow weights for the belt so that your buddy can see you even in our sometimes low visibility conditions.
I recommend you buy the "Fins & Foam" snorkel from me for your first ocean class.
It is important for our conditions here in Northern California to buy a snorkel with some protection from waves on top ("dry"). The Fins and Foam snorkel has this protection, and is high quality and durable.
It also has a feature which most snorkels don't have - an easy way to clip and unclip from the mask (which never opens accidentally in the water). This makes it easier to store your mask in its own case after a dive.
I buy these snorkels wholesale and resell them to you at cost. You won't find a snorkel of this quality for the same price elsewhere.
If you want to buy a different snorkel, any one with protection from waves on top is fine.