You can buy the books whenever, but you have to be level 50 before you can actually use them.
Apart from the Ixal quests as mentioned, the other good ways to level outside of doing levequests are:

1. Grand Company daily turn-ins. These are often better than a single levequest, especially if the item has a star bonus, but you only get to do one per day per class.

2. Just make things. You can get decent EXP with very little effort by quick synthing stacks of cloth and leather. Just check the MB prices before you do this. Often there's a small profit to be made by selling the results, but it'll depend on where the prices are. This is a good opportunity to use company-issue engineering manuals, since you'll rack up base EXP gain fairly quickly this way (and won't get the usual quality-based bonuses.)