Actually, virtually all you will ever need is an el cheapo continuity tester for electric elements. Most of all the other functions on a multi meter will remain unused for years, and I dont know the last time we tried to test windings on an electrric motor. It either runs or it doesnt, and if it doesnt odds are its usually the capacitor (another hard earned tip given away).
Ultrasonic cleaners are great but note:
In order to use for all you would need one with a large tub, not a walmart special just big enough to clean wedding rings or at the most a pair of spectacles! The large ones then are not cheap to buy. We have one that is bigger in toto (for size comarison), than a large sized upright washing machine and the tub still isnt as big as a single laundry tub.
However you probably wouldnt use it all that often for regular machines (therefore not really cost effective to have one and not use often), while they are very handy for cleaning up parts for domestics and autos (just my opinion).
The ultrasonic cleaner is nice to have if you pick it up for the right price from a clearing sale in close to working condition, but I wouldnt rush out to buy a new industrial size one at full price because you can get by perfectly well without one.
Our Test and Tag machine is very useful and used widely, but we also need to have the qualification to be allowed to "drive it".
Otherwise you are loooking at a wide range of conventional tools and a well set up and organised work space. That really is the secret.
Note just because one doesnt necessarily need a range of specialised tools etc its not an open invitation for one and all to take up the opportunity to go into a new "profession" of coffee machine repair. The secret as always is in the level of expertise and experience of the tradesman.
And of course, others may have differing opinions.
PS one of the best and most experienced old school esp machine mechanics I ever knew had, as his main "specialty tool", one of those little screw drivers with the light in the handle that lights up when a circuit is completed. That and a tool box with his good quality spanners. That was all that was required in the end for most run of the mill repairs.