...In Texas, 'caliche' is basically crushed limestone. The soil here in Georgia around where we live has a high clay content. Unless we've had a ton of rain, you can drive over our lawn with no problem. With that kind of base soil, we didn't have any grading to do.
Here in central NM, even the locals can't decide what's caliche or not. On the east side of Albuquerque where I grew up, virtually everything underfoot is some form of decomposed granite (DG). I've seen cases where earthwork contractors who should know better referred to regular old hardpan packed DG as 'caliche', even thought there was virtually no calcium carbonate in it. The crushed limestone you're seeing in Texas is a lot closer to being a proper caliche.
My experience with various clays is limited compared to that with more granular materials, because clay is less common in my area. We'd run into it from time to time on sites closer to the Rio Grande river bottom, but if there was any problem getting it compacted, we could generally stabilize it by adding some DG. (I recall one notable exception, but that's a long story I'll save for another time.)
Clay can present several problems. One is the plasticity when wet...your lawn example. Different clays have different liquid limits. Some will stay stable until they are almost soupy wet, and others will become plastic at a lower water content. Sounds like yours had a high liquid limit. There is a series of tests that can be done on clay to determine the plastic limit and the liquid limit. Using those two numbers, you can get the Plasticity Index. I've never actually run a PI test, but have seen hundreds done in my years of growing up and working in material testing labs. The plastic limit test involves making little clay worms at different moisture contents and noting at what point the clay crumbles when trying to roll a 1/4" diameter worm. It always cracked me up watching grown men sitting at a lab bench making little clay worms. And then baking them in an oven afterward to determine the moisture content. The liquid limit test involved (in simplified terms) putting wet clay in a little dish, cutting a groove in the mud pie, and then counting how many taps of the dish it took to close the groove. Those samples also got baked to determine the moisture content. My school teachers never believed me when I told them my dad made and baked mud pies and worms for a living, lol.
The other clay issue that worries me is expansion. Some (not all) clays will expand when wet, and that can be a big problem under a building. I spent a summer in and around Whiteriver AZ working for an Apache tribe investigating a bunch of government (BIA) housing that was falling apart due to slab cracking. (We saw some houses with 1" wide floor cracks running through multiple rooms. That in turn caused various drywall and roof problems, too.) The tribal officials thought the slabs were settling, causing the cracks. As it turned out, the houses weren't settling, they were rising. They were built on expansive clay, which on its own is not really a problem as long as the clay stays dry. But on these government-built houses that were constructed at the lowest cost possible, the BIA decided not to put rain gutters on the pitched roofs. They also didn't pay close attention to site grading and drainage, so some of the houses had water ponding up right next to the foundation every time it rained or snowed. Of course, those were the houses that were cracking.
Carol, the takeaway from all of this is that from the sound of things, chances are you'll not need to do much in the way of soil preparation for the slab, but making sure the site is graded well to carry water away from the building pad is very important.