In brief
The correct sequence is always the same: first the component's functional requirement — temperature, load, chemical environment, contact with a patient or with food — then the material that satisfies it, and only at the end the process able to shape that material. Reversing the order is the most common and the most expensive mistake.
Among metals the field is wide: nickel superalloys for heat, maraging and tool steels for moulds, stainless for corrosion and hygiene, titanium for strength-to-weight and biocompatibility, aluminium for light weight and conductivity, copper for heat, cobalt-chrome for wear.
In technical ceramics the choice runs through the split between oxides — alumina, zirconia, mullite, cordierite — and non-oxides: silicon carbide, silicon nitride, aluminium nitride, boron nitride, boron carbide. These families behave in opposite ways on thermal shock, conductivity and toughness.
Among polymers the dividing line is continuous service temperature: below 100 °C polyamides are enough, above 200 °C you need PEEK, PEKK and polyetherimides.