When I started in electronics (radio to be more precise) as a hobbyist, all I had was a few hand tools, a 25W soldering iron and a Model7 AVO "borrowed from my father.
Now, 46 years later I look across at my work area and see amongst other things:
Oscilloscope, Telequipment D75, bought 25 years ago for £450
Spectrum analyser, HP 141 series, bought 12 years ago for £900
Signal Generator, HP8640B, free 15 years ago
Frequency counter, Racal 1999, bought 3 years ago for 300euro
Simple PSU, 1 to 20volts 200mA ish, built donkeys years ago from junk, rebuilt several times since.
PSU 12v 8A, on loan from a friend 10+ years ago, (he has probably forgotten he owns it, he also has some of my stuff which I cant say I miss)
Audio Oscillator, free, intercepted on its way to the skip (dumpster to our friends in the USA)
A solderless breadboard, mounted on a case with home made power supplies 5v +12v -12v, variable signal voltage 0 to 12 V, switches, push buttons etc, built 20 years ago from junk (except the breadboards).
DMM, a reasonable one from Korea, bought ? for ?.
So, you dont have to spend a fist full of dollars when you first set out in the hobby, just let the stuff build up over time and as and when you can afford it.
Also dont think of buying the best of something for big money, telling yourself that it will last a lifetime, in 10 years time there will be something much better for much less.
Consider second hand commercial grade stuff say 5 or 10 years old from the big name manufacturers, which the original owners have now upgraded.
My opinion, for what it is worth.
JimB