Thanks @GenTLe for compiling this list. It will probably change links over time but for now this is good.
Anyway, it's not hard to start put together some stuff not spending huge money on Bergeon material.
My initial list would be this:
https://www.aliexpress.com/item/4000648439472.html (the yellow one, the blue one is crap... Don't know the red one).
https://www.aliexpress.com/item/32659049916.html or from Vetus copy. Not the black covered ones which are crap.
https://www.aliexpress.com/item/32996728725.html all useful stuff for managing the bracelets
https://www.aliexpress.com/item/32904751475.html rodico and blower to clean the dials before reassembly
https://www.aliexpress.com/item/33012702129.html screwdrivers
https://www.aliexpress.com/item/33044684615.html tool to sharp the screwdriver head
https://www.aliexpress.com/item/4000416343438.html a 1000/4000 sharpener stone
https://www.aliexpress.com/item/32953797295.html another type of caseback opener (the one with hammered blue paint)
Add also a 10x and a 15x or 20x monocle and some silicon grease (from your hardware store) for the gaskets
Also good to have are few toothpicks in wood.
Eventually:
https://www.aliexpress.com/item/32801078926.html to deal with Rolex casebacks
https://www.aliexpress.com/item/32798194156.html to keep the stem while replacing it and screw it on the crown
https://www.aliexpress.com/item/4000610493318.html hand presser
https://www.aliexpress.com/item/32318726383.html dial protector for hands removing
https://www.aliexpress.com/item/32979924610.html good hands levers
https://www.aliexpress.com/item/32995258148.html oilers
https://www.aliexpress.com/item/4000300583031.html pad holder to de-case the movement
https://www.aliexpress.com/item/4000510712281.html movement holders
https://www.aliexpress.com/item/4000608117086.html a timegrapher to regulate the watch. I prefer the 1900 (which I have, like this: https://www.aliexpress.com/item/32393411616.html) than the 1000 because it has a color display and it's useful to understand where to move the hairspring stud if the movement is out of beat, but the 1000 is ok too.
For the oils it's a mess, you'll need different ones and they should be Moebius, and they are expensive... The most used ones are the HP1300 (9104) and the 9010, then there are various others for the barrel, the pallet fork, the lithium grease...