When I did my open water I already knew I wanted to do deep dives on trimix. The 'forbidden' part of diving was interesting.
The advice I got: Go diving, get experience.
On the question how much experience? I only get the answer, do a lot of diving. But how much? You are now open water, so not ready for technical diving. I bought a normal bcd and single tank as was adviced. Did aow, then divemaster and after 10 months I had 200 dives and said: this is enough to do the full trimixcourse according to standards and bought a backplate, wing and twinset and signed up for adv. nitrox.
Again from others: you are not experienced enough. But how much experience is needed?
1 april (not a joke) I was adv. nitrox certified, 19 april full cave (390 dives), 21 october full trimix and did my first 100m dive (dive 521). 2 years after getting open water certified.
If I got the right advice during my open water, I would never bought a normal bcd and single tank. It was a waste of money.
When I bought the backplate and wing I already had tried to swim a frogkick, that is possible with a bcd also.
With the RIGHT buddies you can progress faster. I did not have that and had to watch youtube movies and try myself. Happely I am more or less an autodidact. But with the right buddies and instructors or mentors it would be more easy.
For the TS: I would do aow first, but with an techinstructor. Why? Tell him about your plans. He can make for example the ppb dive a dive with finkicks also. And then you have AOW and no discussions anymore on boats that you are a 'muppetdiver' (beginner). Try to do all dives from now on in backplate/wing and longhose. Maybe that instructor can be your mentor also or can introduce you to other divers.
Then take a look if cavern is an option or maybe do intro to cave directly, best is if you did the aow with a cave instructor or the aow instructor knows the cave scene well enough to help you further. Here no caverns, so cavern is not possible. People go here directly to intro to cave or full cave (depending on their experience and other certs). I don't do intro to cave in single tank, it is officially allowed, but no, do it in a twinset.
If you want to dive in Florida, you can do cavern first, there are caverns. Same with Mexico.
For full cave in Europe an adv. nitrox cert would be nice because it is almost impossible to do long dives without some deco. Florida is deeper than Mexico also.
Rescue is not required, but some divers find it a usefull course. This all depends on the instructor in my eyes. If you do it with a techinstructor you will learn more than with a typical hurry up resort instructor.
And I don't know what kind of dives you have done till now. But from now on, do different environments, and try to do some dives where your are the leader, you do the navigation, depth, direction, etc. And in EVERY dive you can practise. even if you dive with another inexperienced diver. If you look at a fish, try to be horizontal without moving, or try to do the backkick. You don't need to do a real valvedrill, but try while swimming if you can reach your valves. Closing valves without an alert buddy can be tricky, but only reaching is not a problem. Practise frogkick the whole dive, stay horizontal. Frogkicks, backkicks, horizontal trim and bouyancy can be done also with single tank and normal bcd. No finpivot anymore, but neutral bouyancy. No moving hands.
A drysuit depends on where you live. Here an absolutely need. No technical diving without drysuit. In Mexico a wetsuits is also ok. In Florida I have seen also wetsuits.
You can not even imagine what level of skills is required to reach Advanced trimix level.... in caves. Let me give you my example.
