Story is hard to do in an MMO. Extremely hard.
If you have chapters going on with a timeline, new players end up getting vexed because they will never be able to attain loot items or skills that older players had, and will always be at a disadvantage. One MMO even had a class available only through a limited event, and anyone who started after that event was permanently locked from being able to do that class. If newer players realize they will never amount to what older players who started in beta or just after can get, they will stop playing and head back to WoW. Perhaps some mechanisms can be used to help newer players, such as time travel, or alternate realities.
This said, some MMOs are great at interweaving storyline in single player scenarios and a multiplayer world. The start of LOTRO is one of these where the player first starts in a single player instance. Even the old Everquest 1 starts players off in an instance so they can get the gist of playing in a limited environment before let loose onto Norrath proper. WoW has two decent single player story arcs, the initial DK class creation, and the Wrath Gate arc with the cinematic.
I might give SW:TOR a try, but if I did try a Star Wars MMO, it likely would be SW:G first. It has had a lot of sturm and drang in the past, but as of now, it definitely is a solid MMO, and definitely worth trying out, especially of a person has a Station Access pass.