Party:
Luneth - Warrior
Refia - Thief
Arc - Red Mage
Ingus - Monk

This party worked really well after grinding a few job levels for my thief and monk. Job levels are required to make monks and thieves useful.

The warrior is a solid job pick, dishing out tons of damage and being able to take hits due to their high defense.

The thief is great for using emergency items since they almost always act first due to their high agility stat. I used the thief to steal many potions and elemental damage items that I ended up using later on for my scholar. Needs job levels to deal significant damage.

The red mage is a very versatile class, bringing a lot of utility to your party. They can be used to heal, tank, or deal damage depending on what's required.

Monk starts off really weak, but once you get those job levels it starts to deal a ridiculous amount of damage. The class can potentially save you a bit of gil since you do not require weapons. Monks deal more damage unarmed than with weapons if you have a high enough job level. I found the retaliate skill to be really useful in later stages of the game.

Party:
Luneth - Warrior -> Knight
Refia - Thief
Arc - Red Mage -> Scholar
Ingus - Monk

I can't help but think that I chose the optimal job progressions throughout the game since I was running though the game so smoothly.

The knight was a great upgrade to the warrior. I found myself being saved by my knight on many occasions. Great defense and, with enough job levels, good damage.

I kept my thief since it was at quite a high job level and was dealing some pretty good damage.

I decided to change my Red Mage to a Scholar because of the great synergy between my thief and scholar. My scholar had a seemingly unlimited supply of elemental damage items which deal 2x the damage (due to the scholar's passive effect: pots and damage items become twice as effective). My scholar helped me clear bosses with ease.

Kept the monk since it was also at a high job level and was dealing significant damage.

Party:
Luneth - Knight
Refia - Thief
Arc - Scholar -> Dragoon
Ingus - Monk

Once again, a great party setup for me. All of the bosses were quite easy except for Garuda, who took me 3 tries to beat.

I kept Luneth as a knight rather than changing to a Viking. I really liked the knights passive defense ability which helped me out many times, especially because I did not have a healing job in my party. I wanted to keep Luneth as a knight until the end of the game.

I keep Refia at the back as an emergency item user and occasional item stealer. I did not play the game with a walkthough, so I was completely unaware of the fact that if you have a thief that is job level 71 or above, you can steal a Gungnir from the boss 'Odin'. I had a habit of attempting to steal from every boss in the game, hoping for a rare item, and this was the moment I was waiting for. The moment I stole that weapon from Odin was the moment I realised I needed a Dragoon to make use of it. The Gungnir provides 140 Attack, +10 Strength and +10 Agility, making it a really strong weapon.

I switched Arc from a scholar to a dragoon to fight Garuda, and I kept him as a dragoon until attempting to fight Odin, who I stole the Gungnir from. From that point on I realised the Dragoon was going to be in my party until the end of the game.

I kept Ingus as a monk since he was at such a high job level and was dealing great damage.

Party:
Luneth - Knight
Refia - Thief -> Devout
Arc - Dragoon
Ingus - Monk -> Black Belt

The last job changes I made until the end of the game. All characters were at max job level and were equiped with their job's exclusive ultimate equipment before the point of no return.

The knight was a great class to have with all of the weapons that were found in Eureka. The knight became one of my top damage dealers while having the highest defense as well. The knight proved to be a great end-game class to me and worked wonders throughout the game.

I realised I needed a healer during the final stages of the game, and what better job could I have asked for than the Devout. Thus, Refia was changed to a devout. The cute outfit was a plus.

Arc remained as a Dragoon since I had the Gungnir. I liked the dragoon's jump ability since it prevented my entire party from being wiped after a single spell quite a few times.

I finally upgraded Ingus to a black belt and began grinding for job level 99. The black belt is pretty much a complete upgrade to the monk; I found the black belt's 'boost' ability to be pretty much useless.

End Game: (after defeating the final boss, not including the Iron Giant)

Luneth - Knight Lv.60, JL:99
Refia - Devout Lv.59, JL:99
Arc - Dragoon Lv.59, JL:99
Ingus - Black Belt Lv.59, JL:99