I've only watched a couple (Shingle no kyojin, owari no seraph, 07 ghost) but I'd really like to get into others. Preferably ones that are dubbed. That really helps me. Also lesbian stuff (overt or implied) would be nice, but that isn't so important. Just a plus.
For funny: Baka to Test. There's LGBT characters in it, including a lesbian. Hilarious anime and one of the funniest animes I've ever watched. All the characters have some sort of crazy story behind love or high school crushes. So many funny, dirty jokes. 2 seasons of awesomeness. Also, you might enjoy Mirai Nikki. I guess there's an implied lesbian in it. But there's a lot of great action and it has an interesting story line. Very gory and has some sexually explicit material, but it's still a very good anime imo. Other dubbed action animes I've enjoyed but have no lesbians: Code Geass (well, there's one part that's lesbian-ish, but I think the dub excludes it), K-Project, Kill la Kill, Tokyo Ghoul (only the first season!), Black Butler,
I was gonna suggest Mirai Nikki too. I recently watched it and it shot up to the top of my favorite animes.
I would highly recommend Death Note, Code Geass and Fullmetal Alchemist: Brotherhood to you. Im just not sure if Code Geass is dubbed or not, I always watch anime with subs.
Lez (yuri) anime: https://en.wikipedia.org/wiki/Yuri_(genre)#Yuri_series Some of my fave anime: . Clannad + Clannad: After Story - Angel Beats - Charlotte - K-On! and K-On!! - Naruto + Naruto Shippuden - Shigatsu wa kimi no uso (Your Lie In April) - Sword Art Online - Fullmetal Alchemist: Brotherhood
Van Hellsing has the best dub in my opinion. One of the rare series I actually prefer the dubbed version.
- Another - Elfen Lied - Parasyte - When They Cry - Blood + Those are a couple of my personal favorites not already listed