If you want ezmode gameplay, use Sabin as much as possible, he makes you nearly indestructable once he has Mantra unless you're badly underleveled, especially if you supplement it with some cure/life spells. Edgar is also stupidly, stupidly powerful with the right tools. If you want a challenge, let them sit out when possible. If you REALLY want a challenge, never equip an Esper.
And if you want some funny/awkward storyline, keep Locke and Celes around a lot. Though some of the best parts you're FORCED to use them anyway. And Locke's the only one who can Steal/Mug, which is your only unlimited source of some items, too.
If you use the original SNES version, beware Relm's Sketch bug, it can nuke your saves.