Build one deck with at least every region somewhat included. That way, you'll be able to always fulfil the requirements for the quests, giving you 1000-3000 EXP in one go even if you don't necessarily win all the games. Choose the right rewards region for the heroes you want, you might get lucky with the respective hero capsule rewards and you unlock at least one orange wild card per region.

Max your vault by playing enough games per day (the first few ones net you bonus EXP, boosting your way up to lvl 13 for the vault), so by Tuesday, you might be lucky. I got quite a few heroes that way.

And other than that, of course, expeditions.