I'm thinking about picking up a m43 setup specifically for wildlife pictures.  Just want to get some good magnification and want to be able to start teaching the kids how to use manual settings, the exposure triangle and such.  

I had m43 about 12 years ago, but then moved to Canon Full Frame, then back to my cell phone because I couldn't deal with the big camera and 4 kids at the same time.

I was thinking about the Panasonic 100-300 but can't decide on a body.  Planning to get used with a budget ~$500-$700 or more and maybe picking up one of those Panasonic 20mm lenses, I remember liking those for indoor photos.

What do you all think?  What would you recommend?

Thanks

ETA: Where do you all recommend to buy used?  KEH, B&H, Fred Miranda?

For cheap thrills, the original OM-D E-M1 would be great for your intended usage.  That thing was a wailer for me before I moved over to Fuji for my small-ish sensor stable.  OM-D EM-5 would also be a contender, but not as handy with a long lens in front of it.

I still like KEH, Adorama, or US/Japan/based > 99% feedback users on EBay for used stuff.

That old Nikon 1 system was supposed to be good for small size telephoto wildlife stuff as well.

I have 4 kids as well, and the one camera that was great when they were younger (instead of just a cellphone) was the Nikon Coolpix A.  Fixed 28mm lens equivalent, super small, pop-up fill flash and a high quality DX sensor optimized for that fixed lens.  That thing was awesome.  I still think about picking up another one.  The battery door eventually broke on mine.  Had similar success with the Fuji X-100T, but nothing beat that Coolpix A for streamlined Dad shooting.

Now that the kids are older I usually go light with a Leica M10 or
Fuji X-Pro 3, both with 35 primes.

In my bag is an EM1 and an EM1ii. The EM1 is definitely a bargain. Lens may be a little less bargainish.
The Pen-F was also a bargain find, super lightweight, feels like a 1960s slr.
Lumix brand new is the new hot camera, but a used one might get you there.

I also picked up a brand-new EM10iii from a local realtor who found it too complicated, but it takes decent enough snaps.

I like the idea of an Olympus, I've never had one.

Is it true that you shouldn't use in-body stabilization and lens stabilization at the same time?  Do they cancel each other out, or is that a myth?

It's a myth. They work together to produce smoother, better photos. At least with Canon cameras.

There are times when you don't want to use stabilization at all. But in general, I keep both on.

Oh cool, good to know.

Yeah I think I always turned off stabilization for aircraft pics where they're moving I want a blurry background.

I'm outta practice though, gotta get back into it.

With Olympus you can choose to have both stabilizers on, or only one. It's just a little menu Kung fu.
Used EM1 bodies are inexpensive, and if in good shape, still highly functional. I spent about $200 (keh camera) for mine. It works very nicely.
ETA
EM1ii bodies are more expensive, but a better camera, with dual card slots and more whiz-bang things.

Back in the day I had a complete kit from Vivitar with all prime lenses ranging from 16mm all the way to 400mm. I had like $150 bucks in the entire thing. Was a lot of fun, and a good learning tool.

EDIT: (since I cant delete it to save my dignity.) I just noticed it said M43.  I had an M42 system with the 42mm threaded screw on lenses. Please disregard my brain fart.