The primer pump isn't modeled in game (unlike in BoB WoV2

)
Here's the CloD Hurri startup procedure:
Open your canopy (ok, not necessary)
fuel cock: main tank
mixture: full rich
prop: fully fine
thottle: 1/2 inch open
Magneto 1: on
Magneto 2: on
Shout contact!
Start the engine
The Spitfire startup is the same, only that the fuel cock has to be switched to "on", there's no "main tank" there.