Having access to cure and protect are very useful early on, but it's not necessary to level anything else until lv.30 when you need those classes to access your advanced jobs.

You can grab what classes interest you (including gather and craft classes), but I wouldn't go out of my way to obtain them. You'll be given free airship travel to complete a quest in all the city states at around lv.15. You can simply grab those classes when you make your rounds through then. Level any that you think you can benefit from.

If you are aiming for blackmage, you will want to grab archer and level it to 15 at a minimum.