If you're levelling a tank or healer, you don't need to spam PotD to 60. Once you get the dungeon queue you can use that because the waits are so much shorter. You could also drop the money for a jump potion if you REALLY don't want to wait and go directly to 60.

It's hard to recommend a class because aside from no procs, you didn't really say what you want. Healer wise, AST is the only RNG heavy one. WHM has barely any (one that procs a free Cure II and hardly matters at 70, and another that's so irrelevant most people forget it exists), while SCH sometimes lets you get lucky with a Crit Aldo which is awesome but not necessary to play well (and fairy management, which is work but not random). SCH's big advantage is that you already have it at 60 and can give it a try without having to level it, since it doesn't drastically change between 60 and 70. Course, WHM is an absolute blast to play, especially in dungeons with big pulls because Holy is god tier AoE healer DPS.

Tank wise, PLD gets far more involved past 50 since you get a second combo that's DPS and MP regen focused, a pretty great single target healing spell (used it yesterday to keep a group alive in o8 when both healers got knocked off until the SMN could bring them back up), a ranged magic nuke that you work in for high DPS and gauge boosting, and a couple of spiffy group defense abilities.

Honestly, I find sub 50 play boring on pretty much every class at this point. It's hard to evaluate them at that level because so much stuff is missing. That does make it harder to try to find the right one, unfortunately.