things a new player might have missed

[Niwashi]

No need to run around and look for questgivers, you just need to pay attention and pick up the quests in question when you end up near them - which you will do.

Well, doing every quest you come across will give far too much XP, especially early on, so you outlevel your main quests even faster than you would otherwise. Many players prefer to leave most sidequests for other classes when they won't have the MSQ available.

The problem is that there's no in-game way to distinguish a simple sidequest that doesn't give you anything except a bit of XP and an item or two from a significant one that unlocks a dungeon or game feature. If you want to know which of those sidequests are important to do early on (like which to do with your first class/job), then you need to go to an out-of-game resource, like those lists that Enkidoh linked above.

If quests that unlock features or dungeons had a different quest icon, then having the MSQ send you through the area where you'll see the quest givers would be enough. But they don't. Quest icons currently distinguish only three types of quests: MSQ, repeatable quests, and everything else. I'd like it if they'd further divide that "everything else" category into: quests that unlock features/content, event quests, sidestory quests, and sidequests.