I think the XI should be as follows:
Bairstow/Compton (Both play if 6 batsmen/4 bowlers)
Any two (Assuming 5 bowlers) of Broad/Patel/Finn/Onions/Panesar depending on conditions
Root and Cook are the only two proper openers in the squad, so I'd expect both of them to play. Trott isn't in great form, but keep him at 3. Move everyone up one spot in place of KP, which means Prior at 6 and Bresnan at 7. No reason why Bresnan can't bat at 7 in tests IMO.
Could pick either Bairstow or Compton at 5, think England will stick with Bairstow though after his 95 @ Lord's. If Ian Bell misses any tests then I guess both will play that match anyway.
I'd give Bresnan all 4 tests v India, his batting will be needed, conditions should suit him more than the other seamers, and he averages 33 in the subcontinent with the ball (He's only played 3 tests in Asia though, 2 against Bangladesh). We'll also need Anderson with the new ball, so if we have to drop any bowlers to bring in Patel, it should be Broad IMO, especially if he's bowling the 80mph crap that he was bowling in the final test against SA. Unfortunately, the selectors are incapable of dropping Broad So I fully expect to see the enforcer bowling military medium and picking up 0/120 in every test this winter.
Swann plays all 4 tests if his elbow is okay, Monty is the 2nd spinner if needed, which he probably will be. Patel comes in if there's a pitch which is really turning square. Root can bowl offspin as well. I would've had Tredwell in the squad as well but meh, I guess he'll get called up if any of the spinners are injured.