A Tier

While not essential, these classes are top picks to round out your party.
Priest
Funny enough, you don’t need a dedicated healer when you start out in Dragon Quest III. You can technically cover your healing bases by using your main character and either healing items or the Monster Tamer until you eventually get a Sage in your party. Regardless, if you’re wondering who your third party member should be, I’d suggest “have a little Priest.”
Starting with a Priest has two huge perks. First, a dedicated healer frees up the rest of your party from healing duty, including your incredibly powerful protagonist. Second, a Priest learns so many helpful support skills in the early game that it’ll make virtually any class it later changes to better. Even a Fighter can function like a Final Fantasy-style Paladin when it can remove a slew of status resistances and provide some backup healing when the chips are down.
Oh, and Priests can learn some basic attack magic in the form of Woosh and Swoosh, which it can easily use thanks to the aforementioned full heals on leveling up.
Do keep in mind that if you insist on using both a Mage and a Priest, you may struggle in instances where magic is sealed or you need to use physical attacks. Still, if you’d like to prioritize survival, definitely pick a Priest starting out.
Martial Artist

The Martial Artist’s weaknesses are actually strengths when it comes to the early game of Dragon Quest III. On one hand, they’re extremely picky with equipment, and they’re literally better off fighting bare-handed in the early game until you can find claws for them to use. On the other hand, this means you don’t need to invest a lot of gold into dressing them and you can focus on the rest of your party without grinding. Additionally, the Martial Artist only learns situationally useful skills in the early game. But despite that, skills like Flying Knee and Hawkeye Claw will come quite in handy, especially in the dungeons you’ll need to clear before you can unlock class changing.
There’s honestly not a lot to say about the Martial Artist, as its main function is to just punch nine times out of ten. Still, if you want a dedicated physical attacker on your team, the Martial Artist is a good starting point.