Many cacti have wide shallow roots, but many have a long taproot which can be much larger than the above ground body. Look at your roots and pick a pot based on that. Taproots need a deep pot, short roots need a shallow pot, wide spreading roots can be placed in a shallow pot (ideally a wide one) or a deep one. The reason for "underpotting" is that (desert) cacti generally don't like their roots to stay wet for too long. If you have a lot more soil than roots, that soil will stay wet and your plant may rot. Clay is a great saver of overpotted plants because it allows soil to dry by evaporation far faster than plastic (sometimes too fast!). Some cacti will flower better when underpotted. Another reason is just to save space, most people have more plants than space. If you don't, you soon will :) To a certain extent, I find that using larger pots with a more gritty soil is effective when you have the space, plants develop larger root systems, grow faster, and are more resistant to extreme conditions. The soil can retain moisture for a little longer without ever being wet enough to cause rot. Larger pots work expecially well for larger globulars and columnar cacti which will grow into the root space. Taprooted species should generally be left in cramped conditions, even to the point where they break the pot, they will never develop an extensive fine root system to fill a large pot. Another approach is to use a quite heavy soil, but to water very infrequently, effective for many taprooted species which have weak root systems and need really wet soil to get a good drink, but also need the taproot to be dry most of the time. All getting a bit advanced maybe, but things to think about in the future. Bowl plantings are another acquired skill. Start with tolerant species, and preferably not plants which have wildly differing requirements. Also avoid monsters which will swamp the others before the summer is out. One technique which allows you to ignore nearly all the rules is just to sink individual pots into some kind of substrate in your bowl and cover the whole lot with grit.

Yes, I find those things to be gimmicky. Air plants are fairly slow-growing, but many of the succulents I see in those containers will outgrow them within a year. I want to talk to someone who got one of these tiny terrariums and kept it alive for more than a year. On the other hand, I've started little baby gollum jades from a leaf cutting, and they take well over a year to grow as high as an inch. So there are plants that could work in very small containers.

Personally, sounds like a recipe for disaster. Growing cacti in terrs is often challenging. Give them the light they require and they cook as the terr overheats. Overwater them just once in a terr and that could very well be the end of them. Clay would not be the media of choice, in my opinion. It does not allow for water drainage. Perhaps others either here or on the cacti forum would have some advice. Good luck and happy growing!

It depends on the plants you intend to use. For bog plants a mix of peat moss and perlite is often a good choice. For cacti, the cacti mixes sold in stores works well. For most house plants, standard potting mix may be used. Vermiculite, bark chips, coconut husk chips, and some orchid mixes are also suitable. Do your research and feel free to experiment. Of course please let us all know what you've found worked for you! : )