3D Design software has revolutionized traditional ceramic manufacturing, now it is accessible to hobbyists and potters.
The biggest hurdle to adopting 3D printing is choosing and learning to use a 3D design program. While these are available for tablets and phones, the processing power, multi-function mouse, connectivity and screen of a desktop computer are essential (portable devices are fine for previewing). And you need the desktop computer to handle the 3D slicer software anyway. And 3D design software has decades of maturity on the desktop.
Choosing which 3D package to adopt is generally governed by what those assisting you are using (the complexity of learning this is not something to do alone). As already noted, learning a 3D design software package can be the most overwhelming part of getting into 3D printing. To prevent becoming overwhelmed it is vital to have a reliable helper (a consultant) and be willing to spend some money (e.g. $500 over some months) to guide you through the creation of several things. I recommend using Upwork.com to find a consultant. And Fusion 360 as the designer.
Intimidation by the complexity of this type of software is the biggest obstacle you will face to learning 3D design (for 3D-printing). That being said, the new mission of AutoDesk, the leader in CAD software for 30 years, is to make it easy and universal! Fusion 360 has a lot of advantages. It is a standard. There is a simple learning curve via Tinkercad.com, videos on Youtube, easy online help and many freelancers to hire (at Upwork.com). It is free to qualifying users (teachers, students or people who earn less that $100k/yr), the fact that software of this kind of power and utility is actually available to anyone that wants to try it is amazing. Fusion 360 (and other 3D design products) cannot run 3D printers (3D slicers do that). Fusion 360 is very demanding on the processor and graphics hardware of your computer, typical laptops are not powerful enough.
Popular gurus get millions of views on their videos. Lars Christensen and Tyler Beck are popular contributors. Each of them has plenty of videos to teach you everything you need to know to get started designing for your ceramic production. If you get stuck, there are hundreds of places on line to go to find help. It is helpful if you know how to do a screen recording (e.g. using Screencast-o-Matic) to be able to demonstrate your problem. Getting specific answers to specific problems is a surefire way to progress in your knowledge. The first item to learn is sketching, if you can master that much of what you did will be modifying sketches (e.g. extruding, revolving, sweeping and lofting them).
This slicer ships with, and is recommended for, the Prusa line of 3D printers (when you click to print something in your 3D design software (e.g. Fusion 360) it sends the 3D geometry to your chosen slicer software, that software drives the actual printer). Simplicity and the exact visual reproduction of the printed bed make this a good choice for slicing (slicing is the mathematical process of cutting a 3D object into layers that can be printed successively). Another advantage is that online help for this printer will generally assume the use of this slicer. There are a myriad of settlings and parameters that printing software must respect to adapt to each type of 3D printer and the pairing of the Prusa printers with this slicer will be the best.
3D printing is very important in ceramics, hobby and industry. A slicer is software that slices up a 3D model and runs the printer to lay down each layer.
Standard 3D printing technology (not printing with clay itself) is very useful to potters and ceramic industry in making objects that assist and enable production.
Standard 3D printers (not clay 3D printers) are incredibly useful in ceramic production and design, bringing difficult processes within reach of potters and hobbyists.