Hi. First of all let me say that I'm new to FF. I just picked up a used copy of FFIII w/o the instruction manual, thus ending almost 10 years of procrastination
in actually playing a Final Fantasy game. In 24 hours, I've logged about four hours. I've figured out the basic controls, such as equipping spells and weapons, but there's one thing I can't figure out.

Under the formation menu, when you use the DS stylus to tap the character picture and make it slide to the right a little bit, what purpose does that serve? Is it just to mark a character, or does it actually serve a purpose in gameplay?

If you have a character on the back row of the battle field (aka, the picture icon will be to the right) then that character takes less melee damage, but also deals less. The front lines - left-sided portraits - take more damage, but also deal more.

I'd suggest having Mages on the back row.

Thanks for the info. I'll keep that in mind.
Dark or light mages?

You're welcome

Black and White Mages I would keep at the back. However, if you're not up to the second Crystal and are using a Red Mage, keep it on the front lines.