I LOVE this question! I recently had to REALLY think about what I have on my bench and what is REALLY important to me. Basically I was tasked with setting up a minimum configuration for my bench. The reason for this was my job took me from a 4 bedroom house in the country, where I could spread out, to a high-rise tower in the heart of a big city. LOVE it, but there is NO space for electronics sprawl. I had to condense my bench down into a space that had to fit more/less within the foot print of my beer fridge (which my wife allowed me to keep), and one section of a built-in bookshelf. Here is what it looks like.
That’s the equipment part. This bench strattles my beer fridge you can kinda see at the bottom of the picture. That scope I got for free (I paid it forward by giving my old(er) budget scope to a budding electronics enthusiast) but everything else is pretty budget friendly without compromising TOO much.
Soldering
Good 'ol WES51. ~$100 I think a few years ago.
No surface mount stuff though. 
Some day.
DMMs
I have my trusty Fluke 77IV, I also have a pile of those Harbor Freight $5 ones or whatever in a drawer. They are often free. Not awesome…lot of issues (the cont setting puts enough juice on the line to light an LED for example) but for rough voltage/current meter, they work well enough.
Scope
Just a 4 channel color scope. This one is serious overkill, but it’s the Tek MSO 2024 with the 16 channel MSO deal on it. I got it for free so I figured why not use it.
Power Supply
I have others in storage (off site), but the Long-Wei (giggle) seems to work well for me. If I need other supplies I generally pull AC adapters for odd-ball voltages. I’ve built small DC supplies from 7805’s and switching ICs as well and pull those when I need them. I don’t do a ton of AC so I’ve gone without an AC supply. I do have a waveform generator I made from a 555 if I REALLY need some AC.
I also keep a lot of stuff off of the bench, and pull it out when I need it. On my portion of the bookshelf I’m allowed to use. I have lots of components, buttons, switches, projects that are in process, wire, and all that nonsense. It’s also some homemade tools and equipment that can sometimes replace the good stuff I have in storage. So, power supplies, battery boards, and custom boards that only I have a use for I think 
So, for me this works pretty well. I do small DC sort of projects and the rest is ALL arduino/RaspberryPi stuff so I don’t need a ton of stuff. As far as what every bench should have? A GOOD soldering iron, a DMM, a variable DC supply, set of small and large screw drivers, pliers/cutters and ideally a scope. Even a SUPER cheap or old one is better than not having one. The rest will depend on what type of projects you like to do.
I DO have another scope, high-end bench supplies, meters, function generators and all kinda of really cool goodies, but for 95% of what I do, this is all I need. If I find I need something often or whatever, I generally spin a board using KiCAD/Oshpark.
That’s what I got.
Brian
