Campaign: recommended order and replays
The Prelude plays by itself the first time you boot the game and opens Leon's, Chris's and Jake's campaigns. On Switch, Ada's is available from the start as well.
Order: the first three in any order, and Ada last. Clearing your first campaign gives you 8 skill sets, and clearing all four opens infinite ammo and the epilogue. Ada's story fills the gaps in the other three.
Replays: going back into a cleared campaign keeps each character's weapons and items; New Game starts without them. Skills, Skill Points, emblems, figures, medals and titles are global and never reset. For Professional: Defense and Firearm maxed and an infinite-ammo skill (Infinite Magnum for Leon or Jake, Infinite Shotgun for Chris or Ada).