Dungeons are your best bet for early Thaumaturge if you're inexperienced, and bringing a chocobo in-between them. I started on White Mage and hated leveling Thaumaturge too because I struggled to manage the phases plus tanking mobs at once. Dungeons take care of this for you, but use Quelling Strikes if you're also going to use Raging Strikes or if you seem to be pulling. Interestingly enough, I'm leveling Black Mage as a second main after Bard now that I'm used to DPS.

You'll survive without Swiftcast, it's just useful when someone dies in the middle of a busy battle. Raise has a long cast time and Swiftcast lets you skip that entirely and get right back to healing or dodging.