1 Multimeter
2 Oscilloscope: 2 channels minimum, with delayed sweep*, 4 if you can afford it
2A Logic analyzer (only if you are serious about digital. A good scope will find most bugs a hobbyist can create digitally.
With those two you build anything else you need, for instance:
3 Power supplies. 5V, and +/-15 fixed will get you a long way
4 Audio oscillator
5 Frequency counter
6 Bench amp if into audio. Something like 1-W with a speaker and mic + line inputs
7. RF signal generator, sweepable. Even the audio guys will find this useful for tracking down RF rectification issues.
If seriously into digital design, by that I mean way beyond your typical Arduino build with lost of combinatorial/sequential logic, a logic analyzer is a must-have along with a really good oscope, maybe 400MHz or better. The rest of us should look for 100MHz or better.
Extra credit: Most people, even engineers I have worked with, don;t have a clue what delayed sweep is useful for, and most scopes sold these days don't have it. It allows you to trigger on an event and then, using a second timebase, look at a small segment of the waveform after the tirgger event. This way, if you suspect a glitch sometime after an event, you can trigger on the event, then set the second timebase to something ten or fifty or whatever times faster than the tirggering point and adjust the timebase so that you can see just a chort section of the waveform you triggered on. Then you adjust the delay so you see a magnified segment of a waveform.
