The test equipment you need depends on the type of equipment you will be working on. Let's start with basic equipment.
Power supply; to power the equipment with the correct voltage and current. Should be variable above and below the equipment needs.
Digital volt meter; measure volts, amps resistance. Helpful if it has RMS measurement.
Oscilloscope, dual trace; 50 to 100 MHz depending on the frequency of the equipment being serviced with x1 and x10 probes.
Soldering equipment; both thru-hole and surface mount capabilities.
The following equipment depends on the type of equipment being serviced.
Signal generator; with a calibrated shielded output. Capable of CW, AM, FM etc. Modulation.
Service monitor; capable of monitoring/measuring the output of RF transmitters to .1ppm (parts per million).
Frequency counter; capable of measuring the frequencies of the equipment being serviced.
Most important is a thorough understanding the theory. Know the following: DC, AC, Semiconductors,, Digital, Circuits, Components, Receivers, Transmitters, Antennas, Transmission Lines and Test Equipment. No amount of test equipment will help if you don't know the theory and how to use the test equipment.
The above is focused on servicing 2-way radios. There are many other pieces of equipment that are handy to have like devices to test components (semiconductors, capacitors, inductors etc.). Hope this helps.
Bill