I am building a touring bike that will be used primarily on road but have the capability to handle some offroading. Can anyone tell me if there are conflicts with my desired setup?

Frame: Surly LHT
Fork: Surly LHT
Headset: Cane Creek S-3 (1 1/8”) or Chris King NoThreadSet
Build/Spokes: DT Swiss or Wheelsmith w/ brass nipples
Tires: Specalized Nimbus Armadillos
Rims: Velocity Cliffhanger 36 Hole

Rear Hub: Shimano Deore LX FH-M580 36 Hole
Front Hub: Shimano Deore LX HB-M580 36 Hole

Brake Levers/Shifters: Shimano 105 ST5510
Front Break: Shimano BR550 or Avid Shorty 6
Rear Brake: Shimano BR550 Rear or Avid Shorty 6 Rear

Front Derailleur: Shimano 105 FD-5600 (needs 28.6mm clamp)
Rear Derailluer: Shimano Deore LX RD-M580-GS or RD-M581-GS

Crankset: Shimano 105 FC-5600 (50/39)
Bottom Bracket: Shimano 105 SM-FC5600 English Thread
Cassette: Shimano Deore LX CS-M580 (11-34)
Chain: SRAM PC-991

Seatpost: Unknown
Bars: Unknown
Saddle: Unknown
Stem: Unknown
Pedals: Unknown
Panniers: Unknown
Rack: Unknown

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Which of those two rear derailleurs will work with the STI shifters? Either? If either will work which would be 'better'?

I did read this which explains the difference but I am still totally lost as to how it affects me.

Any input at all would be greatly appreciated!