Just a couple points to add.
cave1 / cave 2 is NOT the same as the traditional. Cavern/intro/apprentice/full cave route. There is also a path for Cave1 though Naui, so the OP needs to be aware the terminology is not all compatible.
I would ask the OP to clarify the short term goal. ..just to "dive past the sign"? ..the lure of the forbidden? ..or to improve diving skills and gear to safely go further into the overhead environment? (Where seeing cool cave stuff is a bonus!). I have also seen ego and peer pressure as motivators, but that does not sounds like the case here.
I also don't necessarily agree with all the minimum #of dives people are quoting. Not everyone is the same, and its skills, capability, and confidence that really matters. Put your flame throwers on safe! I am not suggesting that anyone is ready for overhead training with just 20 dives. What I am saying is that quality of instruction, attitude, feedback, follow up, focus mastery of skills, will all matter, and cannot generally be measured by Dive count. I have also observed divers with >200 OW dives fail to pass an intro class, mostly due to overconfidence and difficulty in unlearning bad habits.
If the OP wants the fastest way to get a full cave cert, then block out some vacation time and head down to Mexico, or N.Fla. Zero-to-hero happens for reason. It's hard to be patient and stick with the safer (better) long term strategy.
Conversely, if you can be patient, and play the "long game", you have to be careful about who you listen to,
I would forget about sidemount for the time being, it will just add unnecessary cost and complexity to your skills advancement. Even if you pay for a SM rig, and instruction, in Monterey, you will have a hard time getting enough dives in to really get good at it. You can actually push off the doubles too, unless you have easy access to that gear. A perfect combo might be a set of double LP50s just to get used to the configuration withought the bulk/weight but I wouldn't go spend the $$ on that.
There are several things you can do to progress and get yourself moving in that direction.
-perfect buoyancy and trim. Remove as much weight as possible. Be horizontal with you and your fins never touching bottom.
-practice good propulsion technique. Frog kick, modified flutter, etc
-learn to use a reel and spools. You can practice on land or OW. Lots of people fumble with this in cave class.
-make sure you have thermal protection sorted out. If your going with dry suit, learn that now in Monterey. So you have that skill down before formal overhead training,
-learn to use a primary and backup lights. Signaling and stowage etc.
-Nitrox, Advance Nitrox Etc. these will really help to have in hand before advancing.
-start diving a "hogarthian" (long hose primary) with your current gear. You can do this even in single tank with a recreational BC.
-if you have not bought your own gear yet, start working on that with an eye on long term goals.
*from a "cave skills" perspective, I would put sidemount diving well below all of the above recommendations to get you ready for formal overhead training.
Point being, you can do a lot now, to make sure you are well prepared for cavern/intro training when you get to that Point.