I am curious what benefit a shop would provide vs a mobile inspection service. I know a lift is helpful in seeing certain parts of the car, and an engine code scanner is very helpful. Any others?
Really depends on the car, but I'd certainly include a good pair of drive-on ramps in the list (so you don't need to put it on a lift) and a strong flashlight or similar light source.
Also, I'd take a magnet depending on the age of the car, so you can detect rust or collision "repairs" that are 90% bondo. If we're talking older or more valuable cars, I'd think a compression and a leakdown tester would come in handy, too.