Keep your clay pots, but use them for the outdoor plants. For indoors, something non-porous like glazed ceramic or, yes,
even plastic would be better for not hosting fungi.
New potting soil should be essentially sterile. But as soon as you moisten it, it becomes a perfect host for any errant spore that floats by. I've used Scott's for years, but lately Vigoro Organic potting soil for a lot of things. It has quite a bit more coconut husk fiber, and less peat moss. I honestly don't know if it makes a difference, except here in FL with our very high humidity in summer I can't use "Moisture Control" potting soil because it stays much too wet. I wonder if the moisture crystals could be what's hosting the fungi - I had a caladium from Home Depot dry out completely on me a month ago, and when I took it out of the pot, the soil was a mass of moldy stuff that would not absorb water. I hosed it off and it floated all around, luckily I was outside and it was a windy day or I'd have breathed in a ton of the stuff . .
For your succulents and mother-in-law's tongue, I'd use a cactus mix or buy a bag of Perlite and mix a bunch of extra in with the potting soil.