Shimano XT Rear Derailleur
The long-cage model is the default choice. It wraps up to 45 teeth of chain, which allows you to be in the small front ring and any cog in back. The plain XT long cage is pictured above. The mid-cage model doesn't wrap as much chain, so if you're in the small front ring, you have to be in the larger half of the rear cassette. If this means beans to you and you want the increased ground clearance and slightly reduced weight of the mid-cager, then get it. If not, just get the long-cage model, and it'll be great.
The 772 Shadow version is Shimano's new low profile design. Looks a little funny but the shifter housing is a more direct line and the lower profile means it's less likely to get snagged on a root or banged on a rock. The 772 movement is like the 771 top normal which is normal normal action not rapid rise reverse action. Shadows look like this:
Both shifts to 36t in back and work up to 10 speed index Shimano road STI systems.
RD 772 GS or SGS shadow. GS means medium cage length in Shimanoese and SGS means long cage. Get the SGS long if you have a triple crank; get the GS medium if you're doing a double or single ring crank.