You better off having scope and signal gen. Simple real life example: yesterday I was working on a router, and all voltages checked out. I pulled out a scope, measured clock crystal, no clock. I now know where to dig further. It lets you see signals, so it is another set of eyes.
Ideal scope for your application is Owon HDS2202S. It is portable, so you can't mess it up in power supplies. It has signal gen. The only down side to it, are its probes, so you will be buying new probe.
You also need LCR meter. It would be like THE money maker in your line of work. I recommend Hantek 1833C.
Both these tools are cheap on Aliexpress and a must have on your bench.
Plus you need multimeter, obviously. If you have a cheap one, I suggest another cheap one. UNI-T UT61E, not the newer one E+, the old one. It has more favorable diode mode voltage, so you will be able to test in circuit mosfets better.