x77 isn't really "required", it's nice for Eidolon hunts because the propa scaffold can be timed to consistently one shot eidolon shields especially now that we have Eternal Logistics and Eternal Onslaught, so you're not relying on RNG procs anymore.
I run a 747 as my "daily driver" and it doesn't steer me wrong, though I'm considering making maybe a 147 for Duviri Circuit specifically. The Phad scaffold, x4x, is one of the best generic mook clearing amps out there. Great ammo economy, good damage, especially if it procs Void and gets a mini magnetize effect.
My setup for context: Operator: Magus Anomaly & Magus Lockdown Amp: Eternal Eradicate & Eternal Logistics.
Anomaly and Lockdown give light grouping and CC to all frames, at all times, regardless of energy constraints. They open the game up in a completely different way and I don't think I will ever switch off of them with the exception of Magus Elevate for things like eidolon hunts and profit taker where CC is irrelevant.
The Eternal combo gives you more than enough damage to kill things, and unlike a lot of the old arcanes they're not percentage based activations. Dump your energy bar, get a huge power spike on demand, always when you want it, always within your control. Combined with Unairu or Madurai, even with Zenurik's AoE slow to a point, that's more than enough damage to take out enemies even well into the steel path. If you're running armor strip or unairu then you will always be able to kill with the operator.
Magus Melt is unique among the operator damage arcanes. Things like Virtuos Trojan and Forge convert damage into their respective types. Magus Melt works like a heat mod for your arcanes, giving you additional bonus damage on top of your void damage, without taking anything away. It's viable because of that, but I just don't find I need that level of firepower enough to give up Anomaly and Lockdown.
Gauss is fantastic, a very tight self contained frame that doesn't need a helminth to function. In fact, fitting a subsume on him is more of a challenge than not. Even if he's next, which isn't a guarantee, it'll be months before he arrives. You can 100% make back the plat for forma and a potato in that time. If he interests you now, go for it.
Yeah, this is an old build but Tadiken is right about Amalgam Organ Shatter. Miniscule critical damage loss for a lot of comfort. 3.8x multiplier down to just 3.7. I'm pretty sure attack speed mods like Quickening/Fury don't apply to glaive throws, but they do obviously matter if you want to use it as a hybrid light/thrown weapon.
"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.
Furious Javelin is powerful, but excessively so. It gives you a huge multiplicative damage bonus with Exalted Blade, but tbh combined with Chromatic Blade you wind up doing so much damage that it's unnecessary.
As you've mentioned, you're building for slash, so you'll want to drop certain mods that don't fill into the slash formula. The really simple version is: Base Damage Mods Count Faction Damage Mods Count
Running elemental mods will do nothing for you. You've got Viral which is a good thought, as viral will multiply slash tick damage, but you're doing all your damage on a single big hit with very little status chance. You can actually drop your elemental mods and pick up a faction mod (primed if you have it, it makes a big difference) and run both critical damage mods. Or you can keep it a little versatile and add in a toxin mod to deal with corpus without having to switch your loadout.
Smite (aka Bane/Faction) mods are important because the actual formula for slash ticks is: 0.35 x "Modded Base Damage" x (1+ Faction bonus) x any additional multipliers. But "Modded Base Damage" also gets multiplied your faction bonus, so base damage mods like pressure point only apply once, but things like smite grineer apply twice, and are multiplicative to base damage.
Here's a build I use when I feel like having my glaive prime out, I usually just bring it on builds where I mostly have it handled with other weapons or abilities but keep it as a backup.
You can also combine this with an external viral source to magnify your bleed damage. Epitaph is the gold standard for glaives since it helps you blanket an area, but a lot of stuff works. These days Nourish is a fantastic option for passive viral priming because it adds viral stacks to everything around you when you take damage.
Welcome back, Tenno. So, I'm sure people have made step by step guides, but the reality is that you're going to want to dip your toe into everything you can that interests you. Even some stuff that doesn't interest you.
The most bog standard, but not incorrect, "new player mid term goal" is "Complete the Star Chart". It's something you'll hear people say all the time, but it's for a good reason. They made it such that you HAVE to do main story quests to progress through the planets now, and you'll by nature learn what every new mission type is, start farming some new gear, dip your toe into every one of the bounty zones. By the time you finish it you'll have a good overview of what the game has to offer, as well as unlocking almost all the alternate game modes, including Arbitrations and Steel Path.
I'd recommend building everything you can along the way, every weapon and every warframe, companions, etc. Just getting a lot of that grunt work done so you can cash in on the mastery rank is nice. MR doesn't equate to skill or proficiency at the game, but until MR16 some content will straight up be locked out which isn't a system I agree with but it's the way it works.
To address a few of the things you asked about specifically; Railjack is mostly a content island, you need it for some quests but it's its own thing. Archwing missions are kind of dead old content, but having access to the Itzal and Amesha archwings themselves are nice because they can be used in other content.
Void Keys don't exist anymore, and have been replaced with Void Relics, which is how you get prime parts to sell for platinum or build to get access to weapons and warframes. It's not my favorite system because it reduces all primes to the same one kind of farm, but it does keep it a lively and healthy community so farming those missions is never hard to do.
Tenno Powers aka Focus Schools will be something you largely do passively these days. They're incredibly powerful and useful now post focus 3.0, which while I have my problems with it I think it was overall a healthy change. Certain new enemy types will just give you sizable chunks of Focus when you kill them, so you no longer have to do eidolon hunts to make any real progress. Zenurik used to be the old golden standard because it gave you access to energy regen and that's not bad, but all of them are useful now. Madurai is my standard equip. You can get a good amount of focus just by playing the Zariman missions, but you get a ton from Duviri as well.
PvP is mostly dead, and Rivens are kind of a mess. Rivens can help certain specific weapons, in certain specific contexts, enable builds that wouldn't otherwise be possible, but in terms of rivens for just raw power increase at what the weapon already does they're kind of irrelevant and not something you need to worry about.