There's a lot you'll have to digest. Mind you, I only know so much, other people like nachobro, GodBeard, Cindi, Anne, etc. (Mix of Neogaf/Bore people I can name off the top of my head) and more can probably explain more in detail.
Anyway, first thing is that there's no reason to pick up a fight stick/arcade stick vs a controller for fighting games. IMO, it should be because you feel comfortable using a stick. Some people prefer stick, other people prefer pad. And controllers in general are cheaper, so if you find out that you prefer pads, you'll likely save money in the long run.
There's three main websites that people use, Arcade Shock
https://arcadeshock.com/, Paradise Arcade,
https://paradisearcadeshop.com/, Focus Attack,
https://focusattack.com/ And then there's the individual companies selling already made arcade sticks, for the U.S. market, such as Hori, Razer, Qanba, etc. The U.S. market primarily deals with JP levers/joysticks due to various reasons, so if you want Korean levers/joysticks or old school American levers/joysticks,(Korea/America/UK, etc sorta followed the same design for levers/joysticks, while Japan went a different route) that's a whole nother level of digging that I have to explain.
In my opinion, realize it's an expensive hobby that you're throwing money at, don't think you'll get better because of it, if anything, you'll get worse because you're either teaching yourself a whole new way to play or relearning it. It takes a large amount of space in your room/apartment.
I have around 6 sticks ( and I lent my friend 3 of them that I'll probably never claim back due to space, not going to drive to pick them up in a pandemic) right now, and my primary one is a etokki Onmi from South Korean made by a guy named Laugh. I don't recommend you getting this because the stick itself is $200 and it cost at least $50 to ship overseas and that was before the pandemic hit. But I love how I can throw shit around on this lever and not feel like I'm breaking it.