The previous post answered your direct question well, but I feel like I should add: arcanes are not going to make nearly as much of a difference as a complete set of the essential mods. Obviously there are some mods you can't get yet (and the ones locked behind daily tribute simply can't be rushed in any way), but there are some staples you should be sure you have. Firstly, make sure you have the basics: Streamline, Intensify, Serration, Hornet Strike, that sort of thing. Those will come just from doing a variety of normal missions, and if you're missing any then just ask someone in your clan or trade chat since most of us have many extra copies of each. Then, make sure you have a good collection of Corrupted (especially all of the Warframe ones) and Nightmare mods. Augur mods are another good addition.

Basically, what I'd suggest is checking out some endgame builds for Warframes and weapons, and making sure that you can do something like them. You'll have to replace some primed mods or especially rare or hard-to-obtain ones, but be sure you at least have a more common version of those mods (ex: Pressure Point instead of Primed Pressure Point, Split Chamber instead of Galvanized Chamber).

In Warframe, mods make the world go 'round. Whichever world that is.

There are NO “must have” Arcanes for a player with under 200 game hours. Approximately.

Assuming you have access to the location you get Molt Augmented from normally and you didn't just buy it with plat (though that is a valid option, I suppose), good arcanes to pick up from the same location are Molt Vigor, Emergence Savior, Emergence Dissipate, Eternal Onslaught, and Cascadia Flare. Slightly situationally more useful (though still good pickups) are Molt Efficiency and Arcane Blessing.

Elsewhere, good arcanes to pick up are Secondary Merciless, Primary & Secondary Dexterity, as well as Primary & Secondary Deadhead. Merciless is what you'll likely be using for most weapons, but Dexterity is nice if you plan to use your melee a lot and the Deadheads are great for specific weapons, especially since the +headshot bonus is a flat amount, meaning it also gives a multi to weapons that ordinarily can't headshot (i.e most AOE weapons of any kind). Again, not a universal slot, but it's good to have the option.

It would also be a wise idea to pick up Secondary Encumber from Otak, and if you don't plan on getting Energize anytime soon, even just a single copy which is perfectly functional, then Arcane Steadfast may be worth the grind.

Personally, my default choices for every warframe that doesn't have particular needs are Guardian and Energize - although if i didn't have access to Energize, i'd probably go for Molt Augmented. Arcane Reaper is also a great substitute for Guardian, as it can be farmed in Duviri. Magus Repair is also very useful, and i've personally come to rely on it a lot.

That said, prioritize filling your mod slots and maxing your mods. They have a much larger influence than arcanes when facturing time spent to acquire them.

"Must Have" being hyperbolic, obviously since you can totally play without any but that's not really a helpful answer to what you're looking for.

Before getting into "what arcanes are good" I think it's important to understand "what role do arcanes serve". Right now warframe is in a phase of its life where builds are all about outsourcing. Finding a build you want that needs to hit a certain breakpoint, or has a certain weakness, and seeing if you can get those stats from some other source, or cover up your weaknesses. Below aren't all the good arcanes in the game, but they're ones I've used regularly or think are worth looking into because they do just that. They allow you to change how you play, and have more fun with build freedom and flexibility.

Warframe Arcanes:

• Arcane Energzie: Yes it's good, but yes it's expensive. It comes out to about 10 energy per second at max rank, I've been around a long time and I don't have a maxed out one, I'd like to some day but energy restoration is less of a big deal these days.
• Arcane Avenger: +45% final additive critical chance. Ie, if in the mod screen you have 55% crit chance, when Avenger is up it straight bumps you to 100%, very useful on a lot of builds that use Combat Discipline to self damage and trigger it.
• Generic Eidolon Weapon Arcanes: Things like Fury, Strike, Acceleration, Rage and Precision. None of them are ones I'd go for first, but they can be useful for allowing you build freedom and diversity.
• Zariman Molt Augmented and Molt Vigor: Both offer final additive strength bonuses. Augmented ramps up and is better suited for things that take longer than an exterminate, but can get you +60% strength, but once you build it up you have it til you die without a timer. Vigor requires an operator cast and only works for a single ability but is +45% strength and is better suited for abilities that can "snapshot" warframe stats, like Gloom or Vex Armor. Abilities where when you cast it, you can either recast it and keep the original strength or it's drain based.

Weapon Arcanes:

• Primary & Secondary Merciless, Deadhead and Dexterity: All of them are cheap to pick up once you have access to weapon arcane adapters, and they radically change how you're able to build your weapons. They functionally all do the same thing with different minor bonuses and different trigger conditions. Merciless triggers on any kill, even DoTs. Deadhead triggers on headshot direct damage kills so not bleeds or burns etc. Dexterity triggers on melee kills so is best suited for a gun you only want to pull out periodically.
• Cascadia Flare: Only applies to secondaries, is one of the nicer weapon arcanes right now. Unlike the previous ones that trigger on kills, Flare triggers on status effect, from any source. As long as you're applying heat procs your secondary will be ramped up, and if it's a high status chance weapon it can even ramp itself up without struggling to kill early enemies.

Operator Arcanes:

• Magus Elevate: If you're worried about dying and you can survive hits, ie you're still relying on health and armor, elevate is basically infinite free healing, as long as your frame isn't getting exploded elevate will heal you back to full pretty much for free in no time.
• Magus Lockdown: Causes you to CC a clump of enemies by void slinging at them. Works on Demolysts for Disruption missions. Huge amount of survivability on any frame loadout, and can root enemies so you can line up headshots for incarnon battery charging regardless of what frame you're bringing.
• Magus Anomaly: Pulls in all enemies in a radius whenever you transfer back into your warframe. Offers loose grouping on literally any warframe. Can be useful for AoE weapons, but also for things like Khora's strangledome or Caliban's armor strip field. It allows you to for free pull enemies anywhere you want them to be, it's not as instant as something like a grouping ability like airburst but there's no cooldown.

Amp Arcanes:

• Eternal Eradicate and Eternal Logistics: Best in slot, hands down. They give your arcane a huge amount of consistent crit chance and crit damage, all you need to do is use your operator abilities.

Dont know about must haves, but there are some easily accessible, Zariman, Lua, Mirror Defense, Steel Path taht will take less time than eidolons

Warframes: Energize, an alternative is the Emergence Dissipate which is super nerfed, but it's more farmable than energize. I'd say the molt arcanes are also all good as they're stat boosts.

Operators: Magus Elevate or Magus Repair are both good as they allow you to heal your warframe. Repair heals % over time, but Elevate restores a flat amount. Repair is better for frames with more health, but I'd say repair is better overall.