I would suggest these steps although you can apply this methodology in any order you need to, if for instance you wish to design a vessel of a particular material and size, and wish to known the maximum safe pressure.
1. What operating pressure do you want to be able to achieve?
2. What shape and dimensions is your vessel going to be? E.g. closed ended cylinder with wall thickness t.
3. How can you estimate the stresses that will be seen in the vessel walls? E.g. for a cylinder you can use Lame equations (or thin walled approximations if applicable) for radial and hoop stresses.
4. What safety factor do you want to apply to the design?
5. What material should you thus make it from (taking into account the maximum stress in the vessel walls, the safety factor, and a suitable yield stress for the material)?
That's pretty simplified, but that's approximately how an engineer would approach the problem. Obviously there are many other factors that you should consider, including corrosion of the vessel material (e.g. an iron container holding sea water...), the fatigue life of the vessel if the pressure or temperature varies considerably, variation of ductility with temperature...the list goes on!