MMOs are not generally noted with their involved stories. Even WoW at its peak was really more about the social experience than it was about the plot. But BioWare has really put something special together here.
If you want to go the traditional route of leveling a character, joining a guild, and so on, you can. Personally, I’m not interested: if I want to apply for a job that I pay to do, I’ll go volunteer at a leper colony. And BioWare anticipated this: while you can’t go it alone on every single quest, there’s plenty of single player content available for you.
It’s not perfect, of course; I ran into the occasional server lag, but it didn’t throw my game off. If you’re into MMOs, or just Star Wars, this might be the game to help you move on from Galaxies being shut down.