Blue Force Gear, Ferro Concepts, Maxpedition and Vertx make some quality pieces; for simple use there are a variety of airsoft makers such as Emerson, Krydex and Wynex that make stuff that should work fine for what you're talking about (ex of a quick search on Mil-Spec Monkey:
https://milspecmonkey.com/store/42-hook-backed?resultsPerPage=99999 and Amazon:
https://www.amazon.com/hook-loop-pouches/s?k=hook+and+loop+pouches). I've got Velcro on the back of my center console and have a Vertx mesh pouch that I like- it's actually empty at the moment as I'm reorganizing a bit.
I bought a pair of metal MOLLE panels off ebay on sale for like $20 that clip onto my headrest posts (these, maybe they'll fit your vehicle or may you can find some designed for whatever you drive:
https://www.ebay.com/itm/165626830192). I have one on the back of the driver's seat with my trauma kit on it. I tried the headrest Velcro panels and did not like the way they fit. I didn't want the style that wrapped around the headrest as I didn't want it to be noticeable from the outside (the access cab windows are tinted and I have black seat covers and went with a black trauma bag with just a red cross on it); the problem was the headrest are curved so the bag didn't fit tightly meaning it didn't engage all of the Velcro. Occasionally I'd hear the Velcro coming lose, especially bouncing around off-road. A actually added an additional strap with a red quick release buckle as extra insurance (I'm probably a bit paranoid about securing gear inside the vehicle from working too many car crashes
but also for off-roading).
I have an Israeli trauma dressing, TQ and extra pair of gloves in my door pocket as well where I can grab them while seated (I can reach behind me and grab the kit off the back if I really need to), but they're in a Ziploc bag- I love Ziplocs and use them for organizing all sorts of stuff. The Ziploc keeps them protected from rain or whatever, you can see the contents, write on them, etc. and you can just grab the top and they rip open easy enough. I do not like anything on my visors, for one I use them as sun visors, but today's car manufacturers make the things so cheaply that they quickly start to sag in my experience (I'm going to have to replace or work on my driver's side soon and they don't put adjustment screws in them like they used to).