"Ease to play effectively and actually pull your own weight" would be a drastically different list. But you seem to mean simplicity. So I'd say, hardest to easiest...
1. Wizard - All the headaches of chosing spells each day combined with the spellbook scribing mechanic.
2. Druid - Managing your companion and summons alone is a lot to track. Add the dumpster diving for wildshape forms and that bookkeeping, and...yeah.
3. Rogue - Being the skill guy, troubleshooter, and point man, not to mention oftentimes the face (I know casters do all of this better again; different list) you really need to know your stuff and have a good sense of when to be wary, not to mention role playing chops (I've never seen a DM just let you roll the dang diplomacy check, sadly). Then you get to combat, where you're super squishy and by design you need to get good melee positioning or find sniping spots. Rogue is very hard to play covering the roles it's expected to cover.
4. Cleric - Prepared caster. Turn Undead really isn't THAT hard, and 95% of the time you can just ignore the whole mechanic. Either because there's no undead, or because you're past the first few levels and it doesn't actually work on an undead of any reasonable threat anyway. Spont. cures makes fulfilling your role super easy.
5. Bard - Similar problems as the rogue, useless in most of the same combat situations, but with some simple point and click save or lose and "sing sing sing to buff the party for +X" stuff to make things easier.
6. Fighter - Without retraining rules, all those feats present many, many different steps to stumble over when you realize too late you made a very bad decision.
7. Sorcerer - Learning how to have a balanced spells known list to cover all the important bases and not load up on too many similar spells is an acquired skill, but at least these guys have RAW retraining rules, unlike poor Fighter.
8. Ranger - Some trickiness in choosing a good companion (very easy to get a redo, though) and favored enemies, and realizing the TWF combat style is a trap. Spellcasting is prepared but too small to be daunting, and you can just make changes the next day if you do make mistakes.
9. Paladin - I'm still not sure what exactly these guys DO... The only real pitfall is not knowing your DM's take on what Lawful Good and your code of conduct means.
10. Monk - Has very few fiddly options to actually make genuinely tough choices over, and all your options suck so bad it's almost impossible to "screw up." Just give the player a sticky note: "Take Improved Natural Attack," and from there it doesn't matter what he chooses, he'll be about the same level of ineffectual.
11. Barbarian - Get power attack and a big weapon. Rage. Rage some more. Yell at someone till they do what you say, or kill them. Can't get much simpler than that.
EDIT: Non-core classes would follow the same general pattern. Prepared casters -> spont casters -> noncasters. More unchangeable options -> less unchangeable options. Genuinely useful options that really hurt to miss -> picking from a giant cesspool of indistinguishable suck.
