I'd recommend:
Ghost in the Shell: Stand Alone Complex
Record of Lodoss War
Claymore
Mezzo
both Vampire Hunter D movies
All are pretty good, aren't too long and I never had any Whiskey Tango Foxtrot moments when I watched them.
I'd avoid FLCL as your first experience since it's pretty ... bizarre.
Ghost in the Shell: Stand Alone Complex
Record of Lodoss War
Claymore
Mezzo
both Vampire Hunter D movies
All are pretty good, aren't too long and I never had any Whiskey Tango Foxtrot moments when I watched them.
I'd avoid FLCL as your first experience since it's pretty ... bizarre.