Are the quests/storyline optional?

Solution 1:

You'll need to do your class quests at a minimum if you want to unlock the full compliment of companions, which is important if you want to keep your crew skills up to date. You'll need to do them through at least level 15 or so to get your ship to be able to get to planets other than the starter areas as well.

Questing is also one of the few reliable ways to bring in credits, and at high levels, skill training becomes extremely pricey.

You can play with a minimum of questing, but the hoops you'll end up jumping through may make it not worth doing.

Solution 2:

if you don't like questing, you're playing the wrong game. I suggest you look for the revival of Star Wars Galaxies (google for it).

But if you're dead set on playing TOR, you can do just the class quests (ignore all the quest givers), and get your exp from PvP or space combat. With the money you get from space combat you should be able to buy your equipment in the AH and keep yourself updated.

You don't even need to do the class quests after you get your companion and ship (about level 10), just do space combat or pvp, but then, you'd be missing out on the best part of this game and what sets it apart from other MMOs.