Doom metal is considerably more melodic than Death metal and the subject matter usually has to do with dealing with loss or love. The tempo is a lot slower as well...Paradise Lost Anathema and My Dying Bride's first albums are good examples of the two combined (i.e. deathdoom).
As far as recommendations (based on the bands you listed):
Anathema - The Silent Enigma (their sound has varied throughout their career but this is the closest to Rapture/StS/etc...)
October Tide - Grey Dawn (although you would probably like Rain Without End...it's a lot darker than Grey Dawn)
Agalloch - The Mantle (not really doom, but has a lot of the same elements as your aforementioned bands)
Katatonia - Sounds of Decay would probably appeal to you as well
Doom metal is a huge genre with a spectrum of sounds and there's a ton of bands that are worth checking out...some personal favorites are:
Paramaecium - Exhumed of the Earth
Saturnus - Paradise Belongs to You
Shape of Despair - Angels of Distress and Shades of...
Tiamat - Clouds
www.doom-metal.com could really help you with any questions.