What is the best material for a compression spring

There is no single best material; the operating environment selects it. For flat wire wave springs the shortlist is short:

1. Carbon steel (AISI 1070/1075) — dry, protected, cost-driven applications.
2. 302 / 304 stainless — the general-purpose default for room-temperature work.
3. 17-7 PH — precipitation hardened, higher strength, and load retention to around 315 °C. The usual step up when a 302 part relaxes in service.
4. 316 stainless — chloride and chemical exposure.
5. Beryllium copper — electrical conductivity and non-magnetic behaviour, which is why it dominates connector work.
6. Inconel X-750 for sustained heat, Inconel 718 where strength at temperature matters more than creep resistance.
7. Hastelloy for aggressive chemistry; titanium where mass is the constraint.

Fix the continuous service temperature and the corrosion condition first, and the list narrows to one or two candidates before any calculation starts.