I would recommend doing everything on the same character unless you have personal reasons to do differently. Like Dan noted, you may get untradeable gear later on that will help you level up alternate jobs, but there is also the fact that a lot of stuff in the game is gated by quests, some of these quests can be a bit tedious.

If you want to experience the story multiple times, more power to you, but it will be way faster to level up a second job (especially if it is a tanking or healing class) if you already unlocked the dungeons while leveling your previous class.

Also, right now you want to be a Summoner, and that, as you say, requires Arc and Thm, but you will really want to take that Thm all the way to 26 for Swiftcast, and you may also want to level Conjurer at minimum to 15 because you will get the odd benefit of leveling 2 jobs simultaneously, since Arc is the only class that can equip two different job crystals (Summoner and Scholar, a healer job.)

...on top of that, the White Mage job requires you to be Arc 15 anyways, so unless you want to level that again with a second character, you may as well do it all with the one character.

Ultimately it is up to you, but it will be way more convenient to do it all with a single character.