I dont know much about dirt driving.
My understanding is that a lot of the upgrades for tarmac would actually be downgrades for dirt.
Example: I think you want softer sways for dirt whereas you want stiffer (to a point) for tarmac. Same with springs!
You might look into some upgraded bushings instead of sways if you're serious about the dirt. There are soft bushings EVERYWHERE (motor mounts, transmission bushings, shifter, steering, suspension pickup points, etc....). For serious driving (tarmac AND dirt) you want those to be less pliable.
Power is good for both
With power though, it makes sense to do as much as possible at once, to save on the tuning costs.
What sort of budget are you looking at?