What size should I use for a 36 -11 casette?

Forgive me, but you are asking the wrong question.The cage size is controlled by the maximum amount of slack chain created by the combination of chain rings AND cassette. This is called "Chain Wrap".To formula for chain wrap is (Big Chain Ring - Small Chain Ring) + (Big cassette Cog - Small Cassette Cog). So if you are using a compact double chain ring (50-34) and a 11-36 cassette the numbers work out to (50 minus 34) + (36 minus 11) or 16 + 25 = 41. This means that if you shift from a big-big combination to a small-small combination, your derailleur has to be able to handle 41 teeth of loose chain, which calls for a long cage. On my bike a have a single 40 tooth chain ring and a 11-42 cassette so the chain wrap works out to (40 - 40) + (42 - 11) = 0 + 31 = 31. So even though I have a huge cassette I only need a medium cage because I have no front derailleur to create more chain wrap.Hope that helps.

what is short, medium.long cage?

It has to do with chain wrap capacity. Small=30t Chainwrap Capacity, Medium=35t, Long=47t. The wrap is just the difference between the number of chain ring teeth plus the difference between the cog teeth. For example a 53/39 with a 12-25 cassette requires 14 + 13 = 27 teeth of wrap capacity needed from the RD.

Will this work with Shimano Ultegra shifter

No, actuation will only work with sram.... The good news is that it will work with both sram 10 speed road and Mtb... Unlike the newer 11 speeds witch are road or mtb specific.

Product Dimensions	12"L x 8"W x 2"H
Manufacturer	SRAM
UPC	757183591480 710845771835 784427964175
Global Trade Identification Number	00710845771835
Item Package Dimensions L x W x H	6.81 x 6.46 x 3.27 inches
Package Weight	0.41 Kilograms
Item Dimensions LxWxH	6.55 x 6.8 x 3.2 inches
Brand Name	SRAM
Warranty Description	Limited Warranty
Model Name	Am Rd Gx Type 2.1 10spd Long Cage Blk
Suggested Users	unisex
Number of Items	1
Part Number	00.7518.080.000
Model Year	2015
Style	Long
Included Components	Rear Deraille
Size	One Size
Sport Type	Cycling

Sram MTB Gx Type 2.1 Long Cage Rear Derailleur - Black, 10-Speed

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