hand tools - screwdrivers (pentalobe, trilobe, 0000 philips at a minimum) a pro tool kit with multiple drivers is good, picks and spudgers and suctions cups as a bare minumum. dental tools - picks, scrapers, spatulas, etc are really great but not required. also highly recommended is a USB volt/amp meter.
organizing stuff - i use 1.5oz stainless steel sauce cups to drop parts and their corresponding screws in while i'm working on a phone. if it need to store pieces or put some work aside, i transfer them to 2"x2" zip top baggies. and 4"x6" pink, anti-static zip top baggies for housing and screens (the smaller baggies fit right inside). magnetic work mats are fine, but all it takes is one sweep of the hand or a something and all that organization is for naught.
i have a push-top dispenser (like you'd find in a doctor's office or nail salon) filled with 99% isopropyl alcohol (IPA) and a supply of lint free wipes (the kind that manicure salons use is great and readily available on amazon). i also have a supply of 1ml to 3ml syringes with needles (available at any pharmacy or amazon) to precisely apply the IPA where needed.
something to heat up the phone as required. hair dryer, a heat gun (i bought a paint stripping heat gun 30 years ago for shrinkwrapping), a heating table or a microwavable heating pad. all depends on how much you need to use it and how much you want to spend. more cost means more features and more heat precision.
also depends on what level of repairs you want to do. i just stick with parts swapping. if you want to do glass work, there are very specialized tools (glass presses, glass removers, laser tables, etc.). the good news is that glass replacement is a high demand and very profitable service. the bad news is the initial cost of equipment is high and the skill level required is mid-range.
if you want to get into component repair, then you're looking at hot air stations, microsoldering equipment and magnification scopes. for the equipment cost and skill level is very high. unless you're looking to open a shop and do this full time, this may not be worth the investment - equipment or training.
figure out what kind of repairs you want to do and what your volume is. based your tools on needs and budget.
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