Complexity in D&D classes is mostly a function of how many other things you have to reference and how much resource management you have to do. Sometimes a core class feature may be somewhat complicated (like rogue sneak attack, which a fair number of people are confused by at first), but you'll get the hang of it quick because you're using it all the time. Spellcasting is the main source of both extra cross-referencing and extra resource management, so spellcaster classes tend to be more complex.
The optimal build for a newbie is not necessarily the least complex, because it might be boring to you or not what you want to play, and complexity can be solved by reading online guides, or just by devoting a little more time to learning the class (which is easy if you are excited to play it).
I think the best starting class is probably a rogue, because it is simple, has no extra resource management, and forces the new player to quickly get a handle on advantage/disadvantage and skills. But if your table is primarily using theater of the mind it can be somewhat frustrating because precise positioning is key to triggering sneak attack, and extra movement is a core class feature.
Barbarians are even simpler than Rogues, you basically just decide when to rage, and none of the subclasses complicate things too much. But it doesn't force you to master core game mechanics the same way, so I'd put it slightly behind Rogue. You do have to keep track of your rages, but I don't think most people will struggle tracking one extra thing (and it's usually easy to remember having used them or not if you forget to mark them down).
Fighter is also pretty simple, arguabley the simplest of all, just make sure to make places on your character sheet to check off when you've used your once per rest abilities Second Wind and Action Surge (and much later Indomitable). I would not argue it is the simplest because the best Fighter subclasses are Battle Master and Eldritch Knight, both of which complicate things.
Monks also don't have spellcasting, but they do have a resource (Ki) that they need to track and which they quickly have lots of different ways to use.
Paladins are half-casters, but they basically end up using most their spell slots for smiting, so they don't need to worry about mastering the spell list. Rangers are also half-casters, but they'll be using most their spell slots for hunters mark early on, so its a nice slow introduction to spellcasting.
Warlocks are a special simple version of dedicated spellcasters who only get a small number of spell slots of one level and mostly end up spamming the Eldritch Blast cantrip. In practice pretty simple, but if you stress over using your few leveled spells optimally it might possibly stress you out.
And this leaves the proper full spellcasters, the Bard, the Cleric, the Druid, the Sorcerer, and the Wizard. These are all a little more complicated than most builds of most other classes. Bards and Sorcerers only get to swap out spells on level ups. Clerics and Druids swap on long rests. Wizards swap on long rests out of a subset (from an extra long spell list) thay they learn on level ups and find in game. Which of these is fundamentally most complicating depends on your personality type. It it harder for you to commit to possibly the wrong decision for several sessions or to make decisions each long rest over spells? Are you an optimizer who, with a whole spell list at your disposal feels the need to learn it all, or are you happy just picking a few that sound cool and letting the dice land where they may?
In any case among the full casters Cleric is probably sort of the simplest, in as much as they don't have much beyond the spells. Druid is similar, but they also get wildshapes, which are something else they have to look up. These are pretty slow to amount to much for most druids, but Moon Druids who get more advanced ones will be scouring the Monster Manual for cool animals to turn into and are easily the most complicated subclass in the game. Bards start out fairly simple, but at high levels they can take spells from any spell list, which depending on personality may make them much simpler or much more complicated for someone. In proper 5e Sorcers got a very limited number of known spells (which might be a complicating or simplifying factor depending on player personality), but 5.5 made them comparable to the other full casters on that front, however they also have Sorcery points and Metamagic to track. However I'd argue that Wizards are probably still the most compicated, since they get sort of the worst of both worlds in terms of complexity on the spell preparing front, since spells are basically their whole deal, and since the Wizard spell list is particularly vast.
Once again, the best for a new player is whatever appeals to you, but I wouldn't attempt the fullcasters (other than maybe Warlock) without a written guide, someone helping you out, or a willingness to just pour over spells at length. Navigating all the spells is just a lot of a lot until you've become familiar with the major ones. Still it's hardly an insurmountable level of complexity if you want to put in some extra work or get some help. Just make sure to find a Wild Shape guide if you're playing Moon Druid and also trying to get a handle on the Druid spells.
