id start by going through the teardown guides on this site and seeing what tools are used in them.
youll also want to make a decision on whether or not you want to have a stock of parts for faster repairs or youll need to find a provider that ships quickly for a faster turn around in repairs.
youll also need to get your hands on a volt\amp meter for trouble shooting.
are you going to be doing board level stuff as well (resistors, caps, diodes)? or just whole components like screens, batteries, logic boards and what not. if youll be doing soldering, thats a whole other ballgame.
a screen programmer and i want to say there is a battery programmer as well?
screen warmer. rubber mat \ screw organizer,
take a look here, this is a bunch of diagnostic stuff that can help also -
https://www.injuredgadgets.com/tools-equ...
https://www.injuredgadgets.com/tools-equ...
https://www.injuredgadgets.com/tools-equ...
i hope this helps!