If you've never tried mobas like League or Dota (or have and disliked them), try Heroes of the Storm.
The learning curve is not as steep for several reasons, foremost being much simpler in-game progression via talents as you level instead of a shop and that XP is shared for the entire team so there is no "last hitting".
Additionally, teamfights are longer meaning there's more interaction and games are shorter meaning there is less of a time commitment per game. Additionally, the "laning" phase is much shorter than in other mobas, meaning you get to the action faster. Finally, there are different maps with various objective phases that help whichever team takes them win the game (for example, Braxis Holdout has points you must hold that eventually will summon a large wave of Zerg to attack enemies).