New player for AOS, need some guidance on what faction to play.

I think ability to control what happens sounds like tzeentch. They have a new book, very cool models imo and really fit the blue playstyle. Just started collecting the army myself as well

Lumineth Realm lord is probably the closest in terms of denying/hindering your opponent from being able to carry out certain actions.

AOS and mtg don't compare well. In mtg you can't see the opponents hands so there are gotchas to how and when you play a card, this is why you don't always play your best card right away. There is also timing because of mana etc. In AOS you see and know everything the opponent can do, and everything is usually on the board already. There are no gotchas really. Nothing to stop you from charging with your strongest unit immediately all the time. In fact some armies play like this exactly.

Imagine an mtg game where you see your opponents entire hand all the time, and everyone has unlimited mana. This is more comparable to AOS.

AOS is closer to chess in many ways.

No army will feel like a blue deck. In fact blue probably is the hardest thing to compare to. In this case I'd just go for aesthetics, so I'd pick idoneth deepkin.

General advice you’ll get: collect what army you think looks the coolest or most fun to paint because you’ll spend a lot more time building and painting than anything else.

There’s not really a 1:1 match for control decks in magic but I’ll give you some armies that are a bit more strategic and tactical in nature since that’s seems a bit closer to what you want.

1. Sylvaneth: more elite army but an army that relies on buff units and synergies and their crazy teleport shenanigans to cripple the opponent’s forces. They’re unique thing is the ability to teleport one of your units to a wyldwood or place of power (which is 1 of 3 terrain features on the board you pick at the start) with some buffs letting you get a bit further out, it lets you attempt to charge an unit in range, and after you attack them you can teleport away before they punch back.

So the trick is you use your army to buff and support one really strong killy unit and teleport it around killing your opponents key pieces. Kind of like picking what creatures to use removal on in magic. You force your opponent to play around what you can do and gradually start gaining more and more advantage until you overwhelm the opponent.

2. Idoneth deepkin: idoneth are an army where the entire range is solid so you can play what you want, polar whatever playstyle you want, and can tune to a meta pretty easily. The strategy however comes from their ability and their tide system.

Armywide they have an ability that forces your opponent to only shoot the closest deepkin unit that’s eligible to be fire on. A lot of armies in the game have some sort of shooting and this forces your opponent to only shoot whatever chaff unit you place in front while you set up for later turns.

Their tide system is what I find to be their most strategic element. Every turn you get a different ability that for the most part reflects where you’d want to be that point in the game.

Turn 1: always treated as in cover so if you do get shot at you have extra defense Turn 2: you can run and shoot or charge. Which lets you essentially move twice and still be able to attack.

Turn 3: this is the big one and what you want to spend turns 1 and 2 preparing for. It’s armywide fight first. In aos combat alternates so you have to pick what unit you want to fight first, then op does, then it goes back to you and so on. This makes combat fair but it lets your opponent weaken your forces before you attack with them. With armywide fight first you can cripple their army before they know what hit them. If you set it up right you can kill off their scariest things and take little damage yourself.

Turn 4: you get to retreat and charge Turn 5: they just repeat.

So while not straight up like control, you can play it to force your opponents to make suboptimal plays to get them in a position you want them in and just take over the game turn 3. So think of turns 1 and 2 like early game control in magic. Those turns you’re either removing smaller threats, counter some spells, or casting card draw spells to find your threat. Turn 3 is like when you drop your big wincon in control and turns 4 and 5 is when your wincon takes over the game and wins

Either Tzeentch or Lumineth. MAYBE Beasts of Chaos, they aren't as good at spellcasting but they are super techy and their Rituals of Ruin can't be denied like spells or invocations.

I just want to give you some adjacent advice. AoS is a game that often takes many hours to play a match, and you are socializing with your opponent the entire time. They are probably not going to enjoy going against an army that has the intention of controlling them in negative ways, people want to be able to do the fun stuff their army allows them to do, then losing can still be a somewhat enjoyable experience. You need to be at least a somewhat fun opponent to make friends and be asked to play future matches, or find like-minded players who want to focus on tough lists and challenges.

Control in aos looks VERY different from aos. Often it means sacrificing a low-worth unit to take up time for your opponent.

Tzeentch, seraphon, hallowheart (a cities of sigmar subfaction) and ossiarch bonereapers are great control armies. Basically you have a mega wizard (or artillery piece) behind tough, recursive, or populous “screens” which keep the opponent sitting in no mans land in combat; while the mega wizard/artillery blows them to bits.

Arkhan the black, lords of change, slann, and sorceress on black dragon, all do a good job of fulfilling a traditional control role.

Other types of control lists are nurgle flies, ironjawz, slaves to darkness, and specific other lists, which seek to charge their opponent in t1, locking them in their deployment zone for the majority of the game. Nurgle flies does this best i think.

Control aos is about giving your opponent 2 bad choices and neither of them mean they win.

Threat range is an important concept

Not the most competitive army, but you could have a look at the Slaves to Darkness - Legion of the First Prince. Be'lakor, Chaos Legionnaires and Furies have some roles to block the opponent.

Disciples of Tzeentch, Seraphon, and Lumineth Realm-Lords are all magic-heavy armies with some careful planning necessary. I've only played Lumineth out of the three, so that would be my recommendation, but any of them would probably do fine as a strategy-intensive and debuff-heavy faction.