I agree with the advice of not buying everything up-front. You know when you need something because you're working and realize you can't do it.
I have built up a minimal lab over the course of the last year, revisiting the electronics hobby I'd embraced as a kid and neglected in my teens and 20s. After the DMM and soldering station, I just acquired as I ran into a concrete need. This is what I ended up with, in approximate order of acquisition:
1. Fluke 87-V handheld DMM
2. Ersa i-Con Nano soldering station (includes 1.6mm chisel tip, i added 2.4mm and 3.2mm chisels and a 2.3mm drag soldering tip)
3. No-name lab PSU (appears to be a Mastech HY3005D)
4. Rigol DS1054Z scope
5. 858D+ hot air rework station (WAY more useful than I expected, well worth the $50)
6. Keithley 197 bench DMM
7. Korad KA3005P lab PSU
8. $20 eBay LCR/component tester
9. cheapie VC830L compact handheld DMM for shits and giggles
Additionally, I purchased various hand tools and supplies as needed, such as (in no particular order)
- good diagonal cutters (the fine kind for clipping PCB component leads, with the little gripper that keeps them from flying across the room)
- various types of wire strippers
- various crimp tools
- component lead former
- top quality solder and flux (I use 0.8mm Kester 63/37 with type 44 rosin flux as my everyday solder, and I have a few others from MG Chemicals, and MG 63/37 solder paste)
- solder reel holders
- solder sucker
- desoldering wick (MG Chemicals, best I've used)
- hobby creek helping hands tool
- trays to hold projects
- Proxxon rotary tool (like Dremel, but far better quality)
- breadboards and leads (commercial jumper leads, and some custom ones like banana-to-header, both male and female, for power, and 3.5mm audio plugs and jacks to male header)
- test leads of all sorts (Fluke TL175 probes, banana-to-minigrabber, BNC-to-minigrabber, banana leads, minigrabber-to-minigrabber)
- antistatic mat and wristband
- power strip with individual switched outlets, for extra safety when working on mains-powered devices
Also, because Switzerland doesn't have any distributors with free shipping, I stocked up on basic components, like resistors, caps, LEDs, pots, and protoboard. I also stocked up significantly on connectors, like headers, matching "dupont" crimp connectors and housings, spade connectors, etc. because the savings on connectors is just massive compared to buying at the local shop. Ordered from China, it's just amazingly cheap, and good enough for beginner tinkering. Then when I'm ready to build the final circuit, I buy good parts from the local distributor.
If I had to prioritize, I'd say the essentials are a good DMM or two, an oscilloscope (SO MUCH you learn with it!), breadboards, and a good quality soldering station (it's a revelation compared to using a bad station or a simple "fire stick"). For many circuits, you can actually get away without a lab PSU, just run off batteries. I also might add the hot air station to the essentials: aside from being great for heat-shrink tubing, it suddenly makes SMD approachable, and it turns out to be handy for other things too, such as desoldering multi-leaded through-hole components.