The new Inna's builds are supposed to be much better. Haven't tested it yet, but will do this week, as I might play monk this season. I suggest you do the same as I will do - check out our builds database for S10 Inna's builds and test them
And which class is the best to Start/Do the seasons journey fastest? Thinking about completeting the conquests...
Since two of the conquests require *multiple classes* anyways, and I'd strongly recommend going for those over the stupidly annoying and difficult "Sprinter" conquest, the answer is: no single class. You'll have to play multiple classes anyways for Guardian (for Conqueror it really doesn't matter, every class can easily do that and the difference is so small that it should solely be based on preference of playstyle). So just start with whatever class you like and then powerlevel a second (or maybe even third) class to get the sets required. You can make up your mind along the way.
If you were to judge all those builds (including the DH), which would you deem the strongest if youre looking for a combination of survivability and damage?
Disclaimer: I haven't tested all of those in-depth and such an assessment would be very subjective anyways. But overall the answer is... it depends for which stage. At different stages in the game, different classes/builds shine.
For example, during leveling (1-70) nothing beats the WD. Once you get the Haedrig's Gift, Marauder (DH) is probably the *most powerful* of the free sets, whereas Raekor is the *fastest* (so while you can farm 1-2 Torments higher with Marauder, Raekor will be faster, and both should net the same loot per hour). Inna's is supposed to be also really good this season, but I haven't tested the new Inna's yet. Once you get to GR50-60, you'll probably have access to other class sets; so between GR50-70 I'd say the Invoker Crusader is by far the "toughest" and the Unhallowed Essence DH will be the "fastest". In terms of damage the differences simply come down to loot (finding an ancient weapon and a few well-rolled pieces is more important than the class/spec). At some point you'll find those builds either lacking damage or survivability; for some this happens sooner (e.g., all barb builds) or later (e.g., Manald Heal wizard or LoN Thorns Crusader). But those builds come with drawbacks: LoN Thorns requires to have the 60% CDR and synchronize the Bombardments with CoE cycle, and MH wizard is super squishy and needs some practice of getting into the playstyle. You might actually be better just continuing a Marauder DH all the way.
That's the essence of this game: it all depends. Yes, some sets are stronger than others, but at the end of the day, your playstyle, your loot (for which build do you have ancient/well-rolled items), and your preference are FAAAAAAAAR more important than following any of the bullshit "meta" trends by which so many people kill the fun of the game for themselves. This game has probably 50 different builds that can easily clear GR60+ (which is sufficient for Conqueror), so I don't get why people always treat this game as if there's only 2 builds that you need to play in order to get anywhere. But I've accepted that people want an answer... so if you desperately need to hear something just go for Marauder DH as it's a decent starter set that let's you do everything you want. But for the love of Diablo, try out other stuff as well. This game has so much diversity, and all the people who claim that their build is 100x better than any other build are straight up destroying this game for everyone else.
As for DH, you said you don't like the playstyle in later seasons - but do you know that the Marauder (i.e., Turret) DH is back in S10? It's even the starter set. Granted, you need to shoot for your turrets to shoot; you can't just put down turrets and go afk. But it's still very close to the S1-S3 Marauder DH I'd say, and very powerful. And also quite decent solo.
All 5 builds you mention are good and interesting; WD Gargantuan and Thorns crusader are the only two of those 5 that work with the starter set (Zuni buffs Gargantuans, and the Akkhan set can be used for a decent thorns build). You could then transition into Firebats or Hammerdin, depending on which class you play. Note that the "CD management" of thorns builds is only important for the Legacy of Nightmares thorns build, which is more difficult to gear anyways; the Invoker or Akkhan thorns builds are no-brainers. But in the end... really... everything works.
WW barb might also be cool, but keep in mind that the starter build is Raekor which means you'll have to play that quite a while before you can transition to WW (need full set and preferably ring+BK weapons).
In terms of damage I'd rate them as follows (I'm excluding the cooldown-heavy LoN thorns build for crusader): Firebats > Hammerdin > Garg > Thorns > WW
And in terms of survivability: Thorns > WW > Garg > Firebats > Hammerdin
For pure solo though, to put this in perspective, I think the Marauder DH would probably be the best of both worlds (decent damage and decent survivability). However: all classes/builds are perfectly viable solo, and while there are a few that have exceptionally high damage (like the lightning Manald Heal wizard) they come with tradeoffs like being a bit more difficult to gear+play, so in the end you should really just go for whatever playstyle you like; the difference in the end might be 5-10 GR levels or so.