Agreed, try League of Legends out first...
You don't get punished as hard for dying, also don't worry about losing a number of times the first time you play. Its all about learning the Hero's and Items with these types of games, and you can only do that by playing several 100 games.
I've played a decent amount of LoL and still haven't tried every single character.
Yeah what cptwin said, also if people start giving you crap for not being a skilled player just shrug it off and keep playing,
also a website called mobafire.com will help with getting a grip on champions skills and a good item build for the champion. once you figure out what champ you want to try just take a look at a guide have a quick read and go hard