No you need to level another class to 15, specifically Arcanist so you can unlock your White Mage job when you hit Lvl 30 with Conjurer.

You can of course level up other classes to try other roles if that's something your interested in but I believe just leveling up the 1 class/job at a time.

As for other skills, you'll be able to use certain skills/spells with your Conjurer/White Mage from certain classes.

For example it's a great idea to lvl up Thaumatage to Lvl26 to get the cross class skill swiftcast, this comes in handy for sending out emergency spells you might need to use.