Regarding stats:
Your stat choices are only important in the short-term. In the late and post game, your stats will always be at or near the cap of (racial base +10) in each stat.

Most stats do not provide any benefit unless raised to at least 16 (Speed I have confirmed to be an exception).

Having a Constitution of 16 or more will get you more hit points. The effect is sort of retroactive; your HP is completely rerolled at every level up (but will always increase at least one point). This means the character won't die as often (but will not completely prevent it).

Intelligence (for Mages) and Piety (for Clerics) make a big difference early on. Speed is important later on.

Be careful with the Fairy race, as it has severe equipment limitations. I only recommend that race for Bishops and Brawlers. (Mage/Alchemist have too few HP as a fairy, Cleric actually has lots of equipment a Fairy can't use.)

Dragonewts are really good. Mental stats and Speed may not be that great, but high Constitution plus a Breath attack (whose power depends on current HP) are useful.

In terms of Ex Skills, Song of Healing is really good early on. Only give it to one character (if you want a second singer, give her a different song).

Remember that it becomes easy to level up new characters later, so don't feel that your choices are set in stone.

For a first party, I recommend some Dragonewts in fighting classes for the front line, and I recommend fitting the Alchemist, and Mage classes in. Also make sure you have one of Thief/Hunter/Bard (don't bother trying to roll a Ninja at the start) and one of Cleric/Valkyrie (don't try rolling a Lord at the start).

Bishops learn their spellls too slowly to be useful until later on. When you do create one, I recommend a Fairy (for more Speed) with Magic Essence (useful for disabling certain enemies with status effects).

Fairy Brawler looks like it may actually work with the AC bonus and a nice Fairy only weapon obtained in an event once you get past the first few dungeons (it's in a dungeon called Hostrana). Dragonewt Brawler also works well due to high stats and the option of breath attacks. Then again, Dragonewt Fighter, Valkyrie, Samurai (might be difficult to create), even Cleric (sacrifice some healing for HP and breath) can all work well.

One more thing: Don't overlook status spells. They are actually useful in this game (though not so much early on when it's still easy).

Thanks for all the tips.
So I'll avoid fairys, since they have an equipment limitation. I assume it has to do with iron.

In any case, I know what I'll roll for now.
Dragonnewt Fighter and Brawler, as you suggested.
Also a cleric, thief, mage and alchemist.

Also, quick question: Thief and Clerics, front or backrow?

Cleric should go in the front row because they can use good armor, plus hammers are actually good weapons.
Thief has worse armor so should go in the back.