Tangent - 1980's Anime I'd Recommend
There's about the first five minutes of the first episode of this eight episode cyberpunk OVA classic for you to take a look at. Four female mercenaries in curvaceous high-tech battle armor face off against the runamock androids of the evil Genom corporation. Owes a heck of a debt to Blade Runner -- the female lead you see singing there is named Priss, for crying out loud -- but the series gives its own twists to that dark and grimy future in a way that only late 1980's anime OVAs can. I still think the Boomer androids from this series are some of the best mechanical designs ever. Oh, and remember, you want the eight episode OVA from AnimEigo and not the inferior late 1990's remake from ADV Films, which features rather blah character designs, a very cool blue color palette, and lousy as all heck Boomer android designs. The series is currently available in a four-disc box set that contains all eight episodes plus a collection of music videos. Just watch out for that English dub; it's a stinker.
Aura Battler Dunbine
Here's the opening theme to a fantasy mecha series that ADV Films has tried to sell unsuccessfully for a few years now, Yoshiyuki "God of Gundam" Tomino's 1983 tragic fantasy epic Aura Battler Dunbine, in which a teenage boy from our world is pulled into the fantasy land of Byston Well, where he is enlisted to help in an ambitious plan of conquest. Despite being over two decades old now, Dunbine still has a very realistic feel, dealing as it does with political alliances, leaders with feet of clay, arms races, and the wary snap judgements of the common people. Plus it has sword-wielding bug-robots. Gotta love the sword-wielding bug robots. ADV Films released the fifty-two episode series on twelve discs, and interestingly the dub is directed by Carl Macek, so it has a very classic feel to it.
Metal Armor Dragonar
And here's the opening to the 1987 Gundam-a-like mecha saga Metal Armor Dragonar, a highly polished series that Sunrise tried to set up as the "next big thing" that year with Gundam's storyline wrapped up with a bow in the wake of Char's Counterattack. It's got extremely solid mechanical designs, likable and kind of infectously goofy heroes, and some pretty good drama. It's not available here in the States (it was never very popular in Japan), but you can download fansubs of the first five episodes (of 48) here and, well, there is a complete Region 0 HK DVD set floating around out there, but A) it's unlicensed and illegal, and B) it's actually kind of hard to come by at this point, too. I especially love that opening sequence, directed by Masami Obari before he became obsessed with boobs. Excellent work.