Anime

Do yourself a favor and checkout Gunbuster (1988) and its loose sequel Diebuster (2004). Gunbuster was directed by Evangelion director Hideaki Anno (and it might be his most concise stand-alone work), while Diebuster was directed by his protege, FLCL director Kazuya Tsurumaki.

Both are just 6 episodes, with fantastic Gainax animation, great soundtracks, and masterful storytelling. I strongly recommend watching the original Gunbuster before Diebuster, though it isn't totally necessary.

I know it may be a hot take, but I am not personally a fan of Gundam. Which seems like a perfect fit but for whatever reason every time I have tried to watch it I just never make it more than a few episodes in.

As someone who is in the process of catching up on all things Gundam before seeing GQuuuuuux (the new Gundam by the creators of FLCL, Diebuster and Evangelion) later this month, I highly recommend giving it another try and sticking with it until at least the second half of the original Mobile Suit Gundam (0079). There are a couple reasons for this:

• The back half of Mobile Suit Gundam is significantly better than the front half, and while the ending is a little bit rushed (the show got cancelled, or something like that), there are a lot of really nice Macross and Evangelion-esque concepts that come into it. Gundam really is significant to the history of anime in general and the mecha genre, and by the time I got to the end of it I finally understood why.
• Watching the original Gundam makes watching Zeta Gundam (the direct sequel) much better, and it's a show that build upon the lore and characters of the original in a fantastic way. I know it's a big ask to suggest that someone watch a 50 episode show in order to watch another (arguably even better) 50 episode show, but Zeta is truly a 1980s anime masterpiece in the same way that Eva is a 1990s anime masterpiece.
• If you ever watch the early Bones mecha anime Eureka Seven, which is pretty good in its own right, you'll be amazed at how much it parallels the story and character development of the original Mobile Suit Gundam.

Gurren Lagann (It seemed okay but I never finished it)

There are a couple of rough episodes in the first half, but I love this show and recommend seeing it through. This is a show where the scale and scope of the story just snowballs into something really big and cool.

Finally, have you watched the SDF Macross movie retelling, Do You Remember Love? Because if not, it's fantastic and worth seeing.