Any manga/anime recommendations?

I would say that anda should give Rozen Maiden a try! That series incorporates all three of those genres into the story and keeps them well-balanced. It's an incredibly fun series, but can also be rather emotional, at times.

Black Cat is also a very good series that applies to your description. =)

Hm, for romance I would recommend Nyan Koi! It's a romance and a comedy, and is really cute too! The World God Only Knows is pretty good too, but if I wouldn't watch the third season. The komik jepang covers it a lot better and komik jepang isn't as rushed.
For action, there is quite a lot in Puella Magi Madoka Magica. It can get very sad though, just a warning!

And for just a wild suggestion, I always recommend the anime Tsuritama to everyone! It's a very good show, and has incredible characters, plot, and the ending just made me cry. It's a very sweet show.

"My Bride is a Mermaid". It's a romantic comedy. It's about a boy named Nagasumi who is saved from drwoning oleh a mermaid named Sun. To avoid being killed atau having Sun be killed, Nagasumi agrees to marry Sun. Overtime Sun's father tried multiple times to have Nagasumi killed due to his over protectiveness of his daughter but Nagasumi always manages to avoid death because of his cinta for Sun. This tampil is rated TV-MA and has high levels of violence, language, and sexual content so watch with caution.