Sworgrader is getting pretty interesting. They've established a multiverse gimmick, and one of the less well-known (but very interesting) Braves is going to be in it:
Read Getter Robo, its TTGL's direct inspiration and it's short as shit (60 chapters for the entire series).
The OVAs are also short too.
Giant Robo is also fucking awesome but less to do with TTGL.
GaoGaiGar is cool too.
GaoGaiGar is EXCELLENT. It's very clinical in its approach, so all that detail makes it very cool. It's also optimistic and uplifting because it's not actually about scorched-earth violence and becoming the best at something; it's more about rescuing and reforming the enemy and having fun with technology. Betterman takes place in the GGG universe, but it's basically a dark version of GGG -- it's important to watch, though, because it appears in GGG FINAL and the sequel manga. Webdiver is similar to GaoGaiGar in that the villains, save for the pure evil big bad, are all brainwashed good guys who have to be rescued. The other Brave series, especially Da Garn, J-Decker, and Goldran, are also worth watching -- I'd suggest Exkaiser and Fighbird too just for their influence on Japanese animation, but they're the type where you can watch the first few episodes, the last few episodes, and any random episodes in between and not miss much. GEAR Fighter Dendoh is also worth watching in full because, much like GaoGaiGar, it has high levels of realism and a lot of interesting character dynamics.
Gurren Lagann is very much in the style of all the 2000s Go Nagai mecha anime. Aside from Getter Robo, the ones that are especially notable are Gaiking 2005 (that's basically an honourary Brave show) and Kotetsushin Jeeg; these two in particular have very cool, WAY over-the-top battles. The Liger manga from the 80s is also good. Xabungle is another anime that had a great influence on Gurren Lagann; however, it focuses more on character development and worldbuilding than action. It proves that goofy Tomino is great Tomino. I really like its mechanical designs that blend analogue and futuristic technology, as well as the mystery of the Innocent and the characters (especially Jiron and Elchi). Overman King Gainer, which I haven't seen yet, is supposed to be similar to Xabungle and Gurren Lagann, so it's going to be worth watching.