As far as comprehensive lists, there have been other threads on pinside about the subject. Lists are also available on the repair sites. This one on the Bally early solid state site:
Non-Specialized Tools Required:
Work Light: clamp style lamp
Screwdrivers: small and medium size, phillips and flat head
Nut Drivers: 1/4", 5/16", and 11/32"
Wrenches: 3/8", 9/16", 5/8" required, other sizes suggested
Allen Wrenches: get an assortment of American sizes
Needle Nose Pliers
Hemostat. Handy for holding parts and springs. Best to have both the curved and straight versions if possible.
Right Angled Screwdriver: both phillips and flat head.
Specialized Tools Required:
These specialized electronics tools are needed..
Alligator clips and wire.
Soldering Iron.
Rosin Core 60/40 Solder.
De-soldering tool.
Digital Multi-Meter (DMM).
Logic Probe.
There are a few tools that seem to almost always come out when I repair besides the DMM and soldering equipment. Number one is my camping LED headlamp - it puts light where I need it. My handheld magnifying glass. A full nutdriver/socket set - you'll use this for leg bolts, backbox bolts, and much more. Another would be my hex head set. Another simple handly tool is a few pieces of plastic flexible tubing. I can't remember which size I.D. it was, but what I use fits snug over the lamps...indispensable for changing out bulbs without breakage.