Gundam has a ton of flavours of Mecha anime depending on what you're looking for, but my recommendation is ALWAYS 08th MS Team. It follows a single unit in a war and that focus on not being about giga-protagonists feels SO refreshing. You're just watching a unit of grunts struggle to survive. Cogs in a machine so vast, that they can't be heroes, just survivors. It also has some SUPER cool fight moments.

Debatable but I think maybe Outlaw Star could count as a mecha anime, the grappler ships kinda control like a mecha

Escaflowne

First off, I'm gonna say Eureka 7 is a show that gets better as it goes on. Consider continuing it. Also, I saw that someone was recommending Brave Bang Bravern which is a favorite of mine. If you want something a little more classic though definitely check out Gunbuster (also known as Aim For the Top). It's only 6 episodes and it's some of the coolest stuff I've ever seen. Really good depiction of time dilation.

Brave Bang Bravern! - A great show and one of the finalists for anime of the year from 2024 in this community. It never fails to escalate the weirdness while not losing touch with the heart and what it means to be a hero.

Planet With reminded me of Gurren Lagann quite a bit and I thought it was fun

The first season of Aldnoah.Zero plotted by Gen Urobochi is a fucking brilliant concept: Think Patlabors piloted by a genius vs high end Gundam fantasy mecha. The second season was meh though.

Speaking of Patlabors, the Patlabor Movie 1 and Patlabor Movie 2 both directed by the great Mamoru Oshii are really great.

It's more like sentai tokusatsu robots (think the Mega Zords from Power Rangers) but SSSS.Gridman is a cool reboot of a vintage Tsuburaya (Ultraman) Productions live action show.

Along similar lines, Samurai Flamenco is another fun take on tokusatsu heroes, complete with a combining sentai robot, which admittedly only shows up towards the end of the only season.

I liked The Big O personally, but it’s very short and highly stylized (if you like noir).

Knights of Sidonia has great visuals and lore ideas but boring storytelling and characters.

Argento Soma had interesting aliens and story but the robots were pretty basic looking.

Bokurano has great visuals and very interesting story, but it has some heavy topics. (Epstein related...) Also I think the manga is better, but the intro to the anime is worth watching just for the song.

Fullmetal Panic has great robot battles, but you might not like the combination of highschool sillyness and serious war story.

Gankutsuou has wonderful visuals and only one Mecha battle in it, but that qualifies it ;). It is an anime adaption of Count Monte Christo

Kenran Butou Sai: The Mars Daybreak has a nice combination of adventure setting and Mecha fights.

FLCL

Attack on Titan (technically speaking, they're fleshy super robots)

Gundam Iron Blooded Orphans

Macross and/or Robotech

Rahxephon

Star Driveeeer

Well, your obvious next move is 1978's tokusatsu Spider-Man.

"Daimidaler: Prince vs. Penguin Empire" definitely counts as Mecha Anime. But that one is more from the WTAF territory.