The main thing I'd stress for anybody playing any job nowadays is just to equip for whatever action you're taking, even if that equipment isn't so great, but that goes double for Red Mage. Ideally, one's character should be the invisible man while playing Red Mage.

Make sure you have whatever Cure Potency stuff you can obtain equipped while curing. Make sure you have whatever Magic Attack Bonus stuff you can obtain equipping while using Elemental Magic. Make sure you have whatever melee stuff you can obtain on while engaged in melee. Make sure you have whatever -DT% stuff you can obtain on whenever things are about to go bad. And so on and so forth for every single action, forever and ever.

This principle has always been important, but the amount of easily obtainable specialized equipment has skyrocketed over the past few years, so it is now more important than ever.