Mecha anime with ideas worth stealing?

I'm planning on, sometime in the future, running a mecha role-playing
game loosely based on the Super Robot Wars series of games (which is
to say, take any giant robot you want, throw it in there, and fight
the evil robots). I haven't decided on a system yet, though I'm
leaning towards FATE; the aspects seem an interesting way to model
different robots' advantages and disadvantages without getting into
the minutiae of something like the Hero system. I also want to have
two basic 'phases' of play: the battle phase, where the pilots are out
in their robots kicking ***, and the social phase, where the pilots
are dealing with their relationship webs (Pilot A is rivals with Pilot
B, who's in love with Pilot C, who's friends with Support Character D,
who's the little sister of Pilot A...)

Naturally, I'm doing some research, and I've asked over on the
rec.arts.frp.advocacy side of things for system recommendations, but I
figured I'd ask here for anime recommendations. I know there's a lot
of good mecha anime out there-- and a lot of not-so-good anime-- but
what would be your top few picks in the 'super robot' and 'real robot'
fields for shows to watch?

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