I'm setting up a hobbyist electronics lab. What kind of equipment
should I buy to equip this lab? My budget is $3000.
"What you need" depends a huge amount on what you plan to do. Radio,
microprocessors, audio, ...
One approach is to buy stuff as your hobby project of the moment
requires - that will tend to match up your equipment to what you are
actually doing, or have done, rather than tying up bunches of money in
things you never use for your particular projects. If you are somewhat
vague about projects, start in with things you need - you can build
power supplies, buy kits to build meters, etc.
Oscilloscope (but there's a huge range, depending on what you plan to
do.) Big differences are Analog .vs. Digital, number of channels, and
speed.
Function generator
Frequency counter (perhaps, depending...)
Spectrum analyzer (perhaps, depending, but even old ones will probably
blow your budget, so perhaps not)
Soldering tools - a combined iron/hot air system is one approach.
Anti-static (not essential for some things, but cheap enough to just do
right once - get a good rubber bench mat and wrist-band)
meter(s) - multimeter, perhaps more than one or some dedicated less
capable meters (advantage being that you can look at two parameters at
once if you have more than one meter). Simpler meters have the advantage
of being dirt cheap. One that does L/C (inductance/capacitance) is
invaluable, especially if getting used parts by scrapping old equipment,
as the markings are often obscure - or if winding your own inductors.
Power supplies
Parts to play with - resistors, capacitors, transistors, diodes,
op-amps, ...
cables, wires, breadboards etc.