Here's my list of tools. I and not any sort of expert and by no means claim it's the best, but I've been able to do mods successfully with it!
I think that's most of it...
If I had to do it over again I think I would buy this kit
https://www.esslinger.com/watch-repair-deluxe-watch-tool-set/
It has basically all the useful stuff short of a cheap amazon crystal press!
from what I've seen, everything is pretty generic and the same.
Here's what I have and it covers pretty much all needs of mine.
I feel like I am about three weeks ahead of you in this journey! Here is what I have decided on:
I went with a new movement (st36, $35). It makes sense to me that I should start out with something that is working and in good shape so I know what things should look like. My approach was to start out small, taking off one or two parts and then putting them back on. Then take off a few more and put them back on, etc. While I am doing this, I am really inspecting them to understand what they do. This is the movement I went with: https://www.amazon.com/dp/B096ZKJFBW?psc=1&ref=ppx_yo2ov_dt_b_product_details
I bought a number of cheap-ish tools off of Amazon. Here are the ones I find myself using:
Watch hand removers. Also works for popping off the cannon pinion. You could use tweezers but I though this is one of those delicate tasks that I should work out on a movement that I don't care if I booger the hands. https://www.amazon.com/dp/B09959K5BW?psc=1&ref=ppx_yo2ov_dt_b_product_details
Brass Tweezers
https://www.amazon.com/dp/B000OVHUSU?psc=1&ref=ppx_yo2ov_dt_b_product_details
Screw Drivers. I did go kind of mid road on the price for these.
https://www.amazon.com/dp/B09Z1XMY74?psc=1&ref=ppx_yo2ov_dt_b_product_details
Tray for parts. These little buggers are tiny so you definitely want to set them in something.
https://www.amazon.com/dp/B07D38YNR5?psc=1&ref=ppx_yo2ov_dt_b_product_details
Hand press tool. Again, I wanted to get used to working with hands that I don't care if I bend.
https://www.amazon.com/dp/B07PVPJ44Y?psc=1&ref=ppx_yo2ov_dt_b_product_details
Mat. Probably not needed if you have another hobby mat
https://www.amazon.com/dp/B07PVPJ44Y?psc=1&ref=ppx_yo2ov_dt_b_product_details
Rodico. Pretty handy stuff
https://www.amazon.com/dp/B077B41Z1C?psc=1&ref=ppx_yo2ov_dt_b_product_details
Movement holders. Honestly, these don't seem the greatest. Maybe poke around a bit for some other ones. But it is needed.
https://www.amazon.com/dp/B08F2PDVDB?psc=1&ref=ppx_yo2ov_dt_b_product_details
Where I struggled the most was magnification. I got these glasses style loupe. They seem OK for inspection and really getting in there to see what is going on but they are not very good for working on the movement:
https://www.amazon.com/dp/B00LX0R220?psc=1&ref=ppx_yo2ov_dt_b_product_details
I ended up picking up this and am pretty happy with it for tinkering around on the movement.
https://www.amazon.com/dp/B09WMZ568Q?psc=1&ref=ppx_yo2ov_dt_b_product_details
Lastly, if you have a nice, big magnet dig it out! Very useful for finding those little parts that go zinging off because you are being too aggressive with your tweezers.
As for oils, I have not bought any yet but I am thinking I need to get some now. After taking apart my movement a few times the balance wheel is not running as smooth any more. I read somewhere that this movement does not come oiled so my current theory is that it just needs some oil.
And no cleaning tools ... yet.
Good luck!