Of course, you can play the DI game. In the beginning, you'll pass elementary training. The DI's creators don't reference the plots of previous Diablo games. So you won't feel like you don't know something, even though this is part of a long game series. You'll be able to play even if you've never tried to play an RPG game. The plot develops very consistently and logically. Plus, you choose the playing difficulty. If you doubt your abilities, I suggest reading a review from the yes gamers site. This will be useful, as there are a lot of tips on completing quests and developing MC's characteristics.
If you’re a casual player, it gets boring quick as almost all the clans require weekly attendance for activities. While you’ll max level quickly and start paragon levels, unless you group you won’t get the great high level gear. Pretty much like all RPG’s.