My tastes lean towards the old, with some new. Gonna keep out some obvious choices because it isn't in what you listed.
Movies:
-Anything Ghibli
-Vampire Hunter D Bloodlust
-Ghost in the Shell
Shows:
-Moribito: Balsa is one of the better female leads in anime. Can't go wrong with this one.
-Blue Gender: Lots of horror elements in this, pretty ruthless with how it kills off characters.
-Escaflowne: Its been a few years, but I remember this being filled to the brim with drama.
-Fate/Zero: Saber is another good female lead, and it has some of the best animation I've seen.
-Cowboy Bebop: Has a little bit of everything, you can't go wrong.
-Outlaw Star: See above.
-Full Metal Alchemist Brotherhood: This is the anime I use to introduce people to the medium.
Witch Hunter Robin: This is another one I haven't seen in ages, but I remember it being heavy on drama, mostly in regards to Robin's duty.
X: This had a lot of character drama in it.
I watch everything in English if given the option so the dubs are good on all of them.