Well... S-type is modelled on SSL consoles, N-Type on Neve, and A-Type on Trident. All of these desks have been used to mix any and all genres you can think of. Also, you're talking about a country-ish set of instruments, but that could cover anything from Shania Twain to The Gaslight Anthem.
Better to think in terms of the kind of sonic character you're after. This is all fairly subtle, but the A-Type is sort of warmer and more bottom-end-y, where the S-Type is typically sort of brighter, with the N-Type somewhere in between. Really, you need to do some experimenting, there's no real prescription for this stuff. To my mind, it's more useful in terms of what you find easiest to mix with. I get along best with the S-Type, whatever the material is.