Test equipment, for learning, is a difficult proposition. I have 2 bench meters, I don't use either one very often. I have a Fluke 189, one of Dave's Brymen BM235s, and one of Dave's 121GWs and a couple of other reasonably high end meters. So, when I want to measure something, which do I choose? None of the above! I reach for the cheapest of the lot, an Aneng 8008. I like that little meter and I find it more than adequate for my electronics projects. No, I wouldn't use it on a 480V switchboard but I don't do that stuff any more.
Be careful you aren't chasing the big kids off a cliff when it comes to spending money on equipment.
I bought the Rigol DS1054Z a couple of years ago just to give my 350 MHz Tektronix 485 a break and I bought a Siglent SDG2082 AWG just because I could. I also bought a Rigol DP832 because I could even though I have gotten along with wall warts and fixed voltage supplies for decades. Because I could, not necessarily because I needed the stuff.
So, given all that stuff, what do I reach for when I want to demonstrate some electronic thing to my grandson? Maybe demonstrate the forced response of an RC circuit? A Bode' Plot perhaps? Well, none of the above! My favorite tool for breadboarding educational projects is my Analog Discovery 2. There's just something about a 27" display for a scope! Seriously, I recommend this to everybody who wants to create a learning environment at a reasonable cost. It does everything! Yes, it's pricey but so is everything else. It does far more and costs somewhat less than my Rigol scope but it includes a dual channel AWG, a dual voltage power supply (current output very limited but better when used with a wall wart) and a bunch of digital stuff including a logic analyzer and protocol debugger. It's pretty amazing!
It's easy to spend a lot of money on test equipment. I suspect it is better to wait for a legitimate need before spending on much of anything. And then see how you can do without it a little bit longer. Make that money squeal before you part with it.
In any event, you probably need 3 DMMs, they don't all need to be high dollar. Think of the common emitter transistor circuit. You would want to measure base current, collector current and Vce. Maybe toss in Vbe... It's an experiment, you don't need 5-1/2 digit meters.