I am basically the local anime queen, constantly watching new shows every season as well as catching my boyfriend up on old good shows that he missed before we started dating.
One anime I constantly rewatch is Heroic Age, a space opera extremely loosely based on the Labors of Heracles and featuring mecha and giant monster battles, as well as a bit of politics and psychics. Highly recommend.
Another oldie but goodie is one of the first anime I ever rented from a video, back when places like Sci-fi channel were licensing all these weird science fiction movies and OVAs. Birdy the Mighty (and the dub of which was surprisingly not bad for a late 90s dub), the original OVA not the new Decode TV series (which I hate). It has fantastic animation that still holds up today despite its dated designs, and I find the story even more engaging as an adult than I did when I was a kid. It's about an alien police offers who accidentally kills a human while out on the job, then must share her body with him while his is repaired, allowing him to continue his life, but also getting her police work done as well. Kind of a buddy cop type show, only the two cops share one body. The biggest reason I prefer the OVA over the TV series is that the male lead actually grows and starts to help Birdy with her mission, whereas in the TV series, he's really just along for the ride and doesn't provide much of any support.
So there's my two recommendations!