What teams should be in all players' 'toolbox' - and in what priority should they be obtained?

Depends on what stage of the game you are :
early on, you should build the teams required for legendary characters, safest being phoenix -> thrawn + palpatine, then empire -> r2 ; then the requirements for cls. Afterwards you can go many ways (fo for bb8 -> requirements for JTR, Jedi for yoda, Phoenix ships for thrawn, ...)

In the late game tho, best thing is to build raid teams that helps you in other part of the game (mainly tw), those being fo, ns, imperial troopers, ...

If i were you, I'd take a look at warrior's "4 pillars" guide, it's the best guide on what to farm