This is a difficult situation. I graduated a few years ago, and they tried to push on us to use a myDAC, buto one liked them. That being said I now have an Analog Devices Analog Discovery (1, not 2) and I find that it is much better. I've tried the JYETech DSO-SHELL and some other cheap digital oscilloscope kits. They do work in a pinch, but they aren't as nice to use, and I am always wondering if I should trust them. Xprotolab Plain is also in a similar category. I find that the UI in all of these are kinda muh, especially when I was spoiled by using Keysight 2000X scopes in school. The only one I really use now is one that has a battery, just because it's isolated and easy to grab.
I also found that having some type of multimeter very helpful, many of the cheap oscilloscope can perform this function, but I found that even a 10 buck meter was very helpful. Also one of the cheap atmegta 328 based LCR like meters is a very useful and comes as a kit. Unfortunately there aren't many cheap multimeter kits, for that I'd say you'd be better off just buying one assembled, as they are much nicer to use, and far cheaper.
I like the idea of building some tools such as a function gen, and a power supply. Before I had a nice function gen I used one of the XR2206 kits. A simple LM317 supply can get you quite far, as long as you don't need anything below 1.2V. For power supplies you'll have to make sure there is enough power for all the tools they might need. Things like the XR2260 need a 9V supply, I found that having a 9V clip to barrel jack very useful for powering most kit tools. Batteries can also be a cheap way to get -voltages if you need them for op amps
As someone who recently set up my own personal lab, something else that you need to consider is supplies. Having a stockpile of resistors, capacitors, and your go to IC (op amp, voltage regulators) are a must. Assume students may fry a few. Now if you are giving them labs to do, you can have them pick up goodie bags with all the parts they need. Also some way to connect them such as bread board.
There is all the necessary tools as well. Wire, wire strippers, flush cutters, tweezers.
All in all it's quite a lot, but when I was setting things up, the first things I had and everything else I got afterward were more quality of life then absolutely necessary.
analog discovery / other oscilloscopes
Power supply,
multimeter (separate from the oscilloscope)
function gen
wire strippers
flush cutters
Consumables
resistor kit
capacitor kit (ceramic and electrolytic)
Protoboard/ breadboard
Soldering (this may be better to have students share)
There are some soldering kits that are relatively cheap that have all these components. They might be a good solution. You could even get a few and let students check them out (although parts may go missing)
iron (some sort of temp control is a must)
wick
sucker
solder
tweezers
iron holder
I have been setting up my lab from scratch over the pass 3 years so I've put a lot of thought into things like this. I'd be happy to answer any questions you may have.