Honestly, Machinist and Ninja both sound like something you might enjoy. Machinist has a lot of varied attacks and how to best use them for your situation can change dramatically between aoe, single target, and your burst window. Ninja is kind of the same way, but melee, you just have te get used to the mudra system. Ninja feels mighty busy at 80, though. It can get kinda rough, especially if you drop in after playing something else for a while
For a tank, it sounds like you might wanna try warrior. There's a bit of tactical play with when to use their gauge, what to spend it on, when to use infuriate for maximum effect. And all tanks have the defensive cooldowns and buster blockers to work with, so that can be neat.
Healers are all pretty samey due to the recent changes, but you might find Astrologian fun, what with the cards and such.
Redmage has utility in heal/raise and a party damage buff. They also have some tactical play to their gauge between aoe, a combo, or a double combo, burning it immediately or saving it for the next fight, etc. But the class can be overall a bit too easy to play. Playing RDM helped me understand some finer points of summoner and blm, though. Like the proper use of ruin 2 or scathe.

For me personally, there's no class I /wouldn't/ recommend trying. Except trying to fight as a DoL or DoH. That's just a bad idea.