I must not have noticed those. Thanks for the info, will take a look next beta round.
Hunting log is pretty easy to see because every mob in your log will have some sort of circle above their names, a bit like if it was a quest mob. So you kill those and it'll display in your chat how many you need and how many you have. There's 10 groups of mobs to kill(sometimes it's just one mob type, sometimes 3), each give about 1-2 quests worth of xp, then when you complete all 10 you get 10x the bonus and it unlocks next tier(which is higher level mobs). Hunting log is class specific so that's quite a decent bit of xp, but not enough for leveling really.
Leves are unlocked from doing the main storyquest up to a certain point, lvl 10ish, you're directed to them. Leves are basically repeatable quests, but you can only do them if you have points, and you only gain 3points a day(I really hope they boost that). You can have up to 100 saved up though so assuming you don't use them on your main, then you can just spam leves on your alts who are out of quests. Leves give fairly poor xp however, other than the first time you do them. Also there's guildhests which are 4man leves, same system. The interesting part about these is if you're grouped, you can get credit for other people's leves too, so it's best done in groups so you all grab a bunch of leves and chain them. Leves themselves are like instanced content in the middle of the real world. You go to the place, press Initiate on the leve log, and it spawns mobs that only people in your group can see and fight. You simply do the quest as usual then you can turn that in for a bit of bonus xp and sometimes item rewards too. There's crafting and gathering leves too but they use the same points so again it's something you want to save up.
Finally the obvious one is to just clear FATE, public quests, they give pretty good xp. It sucks if there's no one around though, especially the boss ones. The ones where you have to kill a bunch of mobs act like normal quests so they can easily be soloed, but the bosses ones are horrible to solo if you even can.
I believe the expectation is once you reach 15, which doesn't take that long even if you're out of quests, you'll chain dungeons and other group content, and it turns into typical FFXI grinding. Oh and also every 5 levels you get class quests, but that's not much xp, it unlocks new spells and shit though.