I've seen new players start and be successful with a wide range of PCs (including druids, who I consider to be the most complex characters in the game). I find that the desire of the player and affinity for that particular character has more to do with success than the actual class -- i.e., if you want to learn the game, and have a character you like, you'll be more successful than if you're playing an "easy" class 'cause that's what the DM selected.
In general, though, I'd rank characters in order of complexity by (1) the number of out-of-play options required, (2) options which require unique or changing mechanics in play, and (3) the number of in-play options available.
For example, I consider the simplest characters (pure class, starting at 1st level) to be fighter, sorcerer, and ranger. Once decisions are made out-of-play, the character generally has a very small number of options to choose from that use simkple mechanics which don't require a lot of calculation on the player's part.
More complex, or moderate difficulty, characters include paladin, rogue, barbarian, and wizard. These either now have multiple simple abilities (paladin), a mechanic which requires regular recalculation (barbarian), have a single mechanic which can be complex to employ (rogues), or have a basic mechanic which must be repeatedly re-evaluated during play (wizards, with daily spell choice).
Most complex characters generally combine the features of the moderate difficulty ones. Thus cleric (spell choice plus melee-spell-turn choices), monk (multiple unique abilities), bard (simple spell choice as sorcerer, but with music, skill, and combat options) and druid (melee and spell challenges like cleric with suboptimal armor plus animal companion and eventual shape management).
This does depend somewhat one spell and feat availability, as the more options there the more complex characters like fighters and sorcerers can become as well (lots of feat choice makes the barbarian seem a simpler choice in comparison, since raging stats can be pre-calculated).
Starting at low level and building also makes all classes less complex that jumping in at high level. Rangers are pretty simple at 1st-4th level, where they have fewer feat options than fighters ... but grow rapidly when animal companions and spells enter the picture. By that time, though, the new player has mastered the earlier mechanics and is ready for new ones. I think that's a very good model for a class ... as it goes up in levels, it should not only offer the player more options, but potentially offer new mechanics for the player to employ to keep playing the same character challenging and interesting, which is probably why prestige classes, feats, and spells are such popular mechanics.