Leveling faster doesn't get you through the story any faster.

The issue with leveling in this game is more often that it's too fast, and (even on a regular server) you'll tend to out-level the quests you're doing unless you divide the XP between multiple jobs. With a preferred server that's even more pronounced, and you need to level several jobs in tandem to be able to go through the content at a decent pace.

Whether that's a good or a bad thing depends on how many jobs you want to start off with while going through the story. If you don't want to choose a job, but level all of them together, then a preferred server is good for that. If you want to focus on just two or three jobs initially, then you're better off on a standard server.

If you want to focus on just a single job, you're kind of out of luck, as you're going to level too fast no matter where you are in that case. The best you can do is avoid all optional content and XP buffs. But you'll miss out on a lot playing that way, so I really don't recommend it, especially for new players. New players should explore and try out everything the game has to offer, not limit themselves like that.