Im new to this. I got a question. Does every character have a different starting story and quest?
Also, has there ever been a discount in monthly subs?
Second question is easy: No, or at least never that I've been aware of. You get a discount if you pay for larger chunks at a time, though. And they had the Annual Pass where you signed up for a year and then got Diablo III and an exclusive mount for free but that's the closest to having a deal tied to a subscription.
Oh, and if you refer-a-friend and they pay for a month you get a free month of game time. I believe you can do this multiple times. That said, if you signed up in the last 30 days and didn't have someone refer you send me a PM (or someone else here you know) with your e-mail address so we can send you a refer-a-friend referral.
As for characters and starting quests the difference races generally start in different zones though do start roughly in the same spot and have very minor differences to the very beginning of the game. But even with that just about every single quest can be done by the other races so if you start a human and run all the way over to where the dwarves start you can do those quests instead if you really wanted to.
Aside from the small handful of quests where you start I don't think there's anything that's race specific within the same faction. There used to be some class specific quests but those are almost entirely gone. The warlocks have their own questline introduced during MoP to get their fire to turn green when they attack but otherwise quests really are only split by faction and even then quests can be shared when they're in neutral locations. I'm sure the quests that aren't shared have the same objectives (collect 12 boar meat!) but have different story reasons or flavor text to tell you why you're doing it for them.
There's no "story" quest that you work on from the start until end game or anything. Most zones have self-contained stories that tie up when you reach the end and then they'll send you on a quest to the next zone over. And with leveling sped up as it is with old content you'll level beyond the quests in a zone before finishing its story in some cases and then you just drop the remaining quests and move on (or finish the quests anyhow if you want to see that story come to its end),