There are a few options for knocking out the daily missions!
Randoms and Ranked both provide quite a bit of Base XP since they're PvP modes with higher rewards.
Co-Op is also available, but does have lower rewards in general. However, you can play matches much faster (usually around 5 minutes a battle) so the Base XP can rack up over time. The average Random Battle might give you 1,000+ XP, but it can take two or three times as long as a Co-Op battle might last.
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As for learning about how Base XP is earned and how to get the most out of your games, definitely check out this video: