Anime

Two thumbs up for Gurren Lagan and Code Geass. Seconding the suggestions for Rahxephon and Escaflowne. ~~Surprised nobody has mentioned Evangelion (unless~~ I'm blind, ~~in which case~~ disregard). Full Metal Panic is another favorite of mine. I haven't watched Gasaraki in forever but I remember it keeping me on the edge of my seat.

Without knowing what other Gundam you've seen aside from WfM, I'm going to make my default recommendation: start at the beginning and watch in production order. The core Universal Century arc of 1st Gundam, Zeta, Double Zeta, and Char's Counterattack laid the foundation for everything that came after. From there, you can continue on with UC if that caught your attention with a bunch of excellent OVAs and a full series that's far future enough that it's only barely connected. (Crossbone animation when Sunrise???) Again, I recommend keeping production order.

Or you can jump into any alternate universe that catches your eye. G is a big tonal change but stands well on its own. Wing was my entry point, and I do have the feels for it, but objectively I don't think it's holds up very well. X has some dedicated fans but I've always found it kind of middling. Turn A is absolutely beautiful. Seed is extensive and polarizing. OO was pretty good. IBO is like a gut punch but worth it. And then there's the Build universe, which has some awesome entries and some that weren't so good.

tl;dr Want more Gundam? Watch more Gundam. 😁

Mobile Police Patlabor is a classic Mecha series from the late 80's.

Sounds like you would be into Ghost in the Shell as well.

Eureka Seven

Mechs on surfboards, politics, main characters are young trying to fight the power.

Gargantia? Although that's kind of more Gundam meets Nausicaa. The elements you mention are present, but more background than foreground. Maybe save it until you've spent some time with the others and want to branch out a little further from the basic premise.

Gundams

The Origin

Thunderbolt: December Sky

0083: Stardust Memory

Unicorn

08th MS Team - A Battle with the Third Dimension

Hathaway

Char's Counterattack

SEED CE73: Stargazer

G Gundam

00 The Movie: A Wakening of the Trailblazer

Wing

Non-Gundams

Eureka Seven

Macross Frontier

Ghost in the Shell

Move Code Geass and Gurren Lagann to the Tengen Toppa the list

Code Geass and Gurren Lagan were going to be my two recommendations. I think Code Geass is a more interesting story (although the end is hit or miss). Gurren Lagan though is juat a lot of fun (and not as serious as Gundam).

• Kuromukuro
• Aldonah.Zero
• Sidonia

Forgot about Granbelm. I personally think it's an absolute gem.

Its less gundam mechas and more space opera masterpiece with mechas, but i recommend Mugen no Ryvius/Infinite Ryvius. Imagine lord of the flies but in space.

https://myanimelist.net/anime/593/Mugen_no_Ryvius

Edit: also eureka seven is a master piece too. Not Ao though, dont bother.

Ideon hits most of the points you mentioned. Make sure to watch the movie too for the proper ending.

I am far from a connoisseur in the genre. The only mecha I have really watched is Gundam Wing, Escaflowne, Evangelion, and more recently, Bravern. Some thoughts...

• Gundam Wing is an absolute classic for me since I was in my formative years back when it was airing. It is a good mix of politics, drama, war, and some romance. It also has a compelling enough ensemble cast that you aren't bored when the story spends some time away from certain characters. I have no idea where this show fits into the great Gundam-verse, but I think it was easy enough to follow on its own, at least it was for me as a teenager (so maybe I just didn't care? idk).
• Escaflowne is a different feel. It feels more like a shoujo series in that the main character is female and is embroiled in a love triangle with two guys (the gentleman and the bad boy more or less). It also incorporates fantasy elements into the story, being an early example of an isekai, before it was even called that. The story gets a bit weird at the end, but it is full of good character drama and checks off a lot of your list; war, romance, politics.
• Bravern is a parody of the genre and a comedy. It is honestly probably one of the most fun series I have watched in the past year. It will swing between the grim realities of war (death, destruction, torture...) in one scene and then be cracking jokes in the next. It is hard to truly describe with words what watching Bravern is like. It is an interesting blend of the two types of mecha out there: the real mecha where these things are machines and tools used by humans, and the super robot variety in which there is one superpowered robot that is sentient and helps to save humanity.

It's tangential but RahXephon has always been one of my favorites.

Some that I didn't see anyone else mention.

Broken blade is the only mecha my spouse could watch. I loved it personally.

Zegapain for an interesting world concept.

Aldnoah zero for a flip with the bad guys with gundams.

its a bit different than the traditional political stuff found instandard Mecha, but give Majestic Prince a shot.

mecha about humanity fighting against an unknown force thats superior. follows a group of 5 misfits and their crew. Character Designs by Hirai Hisashi (the guy who did character designs for Gundam Seed).

Show starts off slow, but gets a lot better

The second season of Iron Blooded Orphans is a good follow-up to the first, and certainly contains the themes you're looking for.

How has no one mentioned "The Big O"?

Its basically bruce wayne with a gundam suit!

How no one has recommended the Macross series is beyond me. It's not mech vs. mech, but mech vs. alien.

I like Macross: Frontier most, but I'd probably just go through them in order.

Legend of the Galactic Heroes is pretty good too, although it's less mecha and more strategy.

No mecha, but for War is Bad and child soldiers I feel like you can't do better than Vinland Saga. Its a story about war, the trauma it causes, and recovering from that trauma. Its a historical war manga by someone who abhors violence and its stunningly beautiful

No one's mentioned Argevollen yet, so I'll put it forward.

Probably unexpected suggestions, but these anime totally fit your criteria:

• Guilty Crown
• Kill La Kill

Guilty Crown is hitting a lot of the themes you've spoken of, but perhaps not in the ways you'd expect. It's not particularly a "mecha" anime but as you say, there's a macguffin that serves as a similar driving force of much of the spectacle and combat sequences.

Kill La Kill comes from the same studio as Gurren Lagann so it's no surprise that it kinda strikes a lot of the same chords, but here the mechas are replaced with.... getting naked? no wait come back i swear-

And, I'd be lacking if I didn't recommend this even though it's not anime:

• RWBY

RWBY is an excellent show - give the animation time, it gets better very fast. Season 1 flies by with short episodes so you don't really have to deal with the lower animation quality for very long. The writing is splendind, the music is outstanding, and it strikes every note you've mentioned. I feel deep, deep feelings for the cast of characters, and I have no doubt you will too.

~~cross ange~~, star driver

edit: you already had one in your list.