I loooved Lip Service and OITNB. And the lesbian story in Mistresses. I've heard about Orphan Black and The Good Wife but haven't watched those series yet.
Last Tango In Halifax has a main lesbian couple (portrayed realistically instead of being relegated to a stereotype thank god)
Faking It is a great series. I highly recommend it. It's written well, the cast chemistry is superb, and a lot of the one liners are priceless.
I've seen a lot of them, but I honestly say I haven't seen any that I can really relate to. The closest might have been in the show, 'United States of Tara', with the one brother. But as for gay male characters, I never seem to have much/anything in common with them, that draws me in. Maybe I'll check out Faking It. Is there a variety of characters, or are they kinda stereotyped? That's my main problem, with most shows I've seen.
I second (third? fourth??) Orphan Black and Faking It, and I highly recommend In The Flesh as well. Easily one of favourite TV shows of all time, if not my favourite over all.