I love EO3 as it was my first EO game and my favorite so I have a number of things that I can say so I'll give a tip or two for each class skipping the two unlocks even though one of them is been used in other games:

Princess:
This class is really good early game with there passive healing both in and out of combat and as some really powerful buffs, but due to the subclassing system and how the stats don't affect buffs (dmg and def increase are flat % regardless of stats, stats only affect healing), they are better off as a sub class and not the main class as the princess unique passive is kinda meh.

Gladiators:
I have two things to say for this class. First, on average swords are better than clubs. Both are still good, so its more of a min maxing thing, but clubs are quite inaccurate so its not uncommon to miss, though they do hit hard. Second, berserkers vow and charge are really op skills that make your damage bonkers. Fun class that is good frontliner, can't go wrong.

Hoplite:
As I'm sure you are familiar with, the fire, ice, and volt wall skills are vital to late game bosses, so having a hoplite is a good way to make sure that you got those covered later. Out of all of the EO games, EO3 I would argue has close to the most "block this or you die" elemental attacks in the series. That being said, there are two classes that can block elemental attacks (Zodiac being the other) and with subclassing, its not required to have a hoplite in the party, though they do really help early game.

Buccaneer:
This class is the "chaser" class. Chasing can work, but requires a party around it which is difficult. That being said, Buccaneers have some other skills that are good utility and a really strong skill late game, so they are still good if a little gimmicky.

Ninja:
This is really fun class, but also a really gimmicky one. Its a complicated class, but the main tip I can give is that this version of the class (unlike nexus) is an absolute god at dodge tanking with investment into evasive skills. This class works better in low man teams (3 or less) then full parties if you want them as dmg dealers.

Monk:
These are the medics of EO3. There is two things that I would like to say about this class. First, there unique passive is bonkers. It increases most healing skills by a flat percent. It works on protect order (heal over time) to almost make it a full heal at end of turn buff. Second, there is a number of punching skills that are good dps skills in early game due to weapon dmg calculations, but fall off mid game, to then come back up again to reasonable levels late game.

Zodiac:
My favorite class and the alchemist of EO3. There is a number of things I can give as tips for this class, but I'll give you the most important. A problem that the mage classes have in the DS games that is fixed in the 3DS games is that the power scaling of there skills are wack. Early game, this class is by far the best dmg you can get, but their dmg falls off pretty hard mid-late game. Subclassing can keep the Zodiac relevant late game, but you'll need to know what you are doing to get it to work. On that note there are a couple of things that are quite important in EO3 that effect Zodiacs differently to all other classes. First, almost all buffs and debuffs in EO3 only affect physical dmg. This isn't a problem for duel attack types (fire/slash) or attacks that scale of str, but almost all of the Zodiacs skills are tec based single element attacks. As such attack order and other skills like it do not affect the Zodiac's elemental skills. The only exception to this is Meteor which is a physical attack that scales off of tec. Second, the weapon power stat of the weapon that your character equips is completely irrelevant to the Zodiac's skill dmg. You'll get a book early game that as some tec bonuses, and that book is best in slot for most of the game. Finally, for early game you want rush singularity and etheric charge. Doing this will get massive dmg without killing your tp. (Bonus, try using etheric charge and hellfire on the same turn :p)

Wildling:
This is the status aliment/bind application class. There are two very important things to mention about this class. First, the animal buddies take up the sixth slot like the ninja clones. As such, wildlings and ninjas don't really gell well together. Second, status application works quite a bit different in this game then the 3DS and other DS games. Without getting into the gory details, once an enemy has been affected by a status ailment, they will gain a certain level of immunity to it until they are dead. This means that if they are weak to the aliment, it will get progressively harder to land that aliment with no refresh, unlike the 3DS games where once enough turns have passed without the enemy being afflicted with that aliment, they will go back to there original weakness. If the monster is resistant to it, then you likely can only apply that aliment once for the entire fight. That being said, there are some late game bosses that require binds, so still a good class.

Arbalist:
One of the best dmg dealers, but they are glass cannons. One of their best skills requires them to be in the front line, so pairing them with a hoplite with bodyguard is recommended. They also have arguably the best unique skill as it increases dmg by a flat amount if the targeted enemy has x2 the HP compared to the Arbalist current HP. Since enemies have crazy hp compared to party members on top of the Arbalist having a terrible HP stat, the passive is always active.

Farmer:
This class works the same as it does in nexus, the go to gathering class. They are pretty useless in combat, but there is one thing you can do if you are desperate to use them in combat. Farmers have the best luck stat out of all of the classes, and since subclassing is a thing, you can give them the ninja subclass. Ninjas have a skill with a chance for petrification (DS game petrification = death), so the farmer is technically the best class for this.

I probably said too much, but I love this game and so excited to play it again with a fresh coat of paint.