There is never one perfect lineup and there are no hard and fast rules. There are lots of generalities, there is instinct, and there is the "playing the hot hand".
I like the idea of having Ichiro and Jeter at the top of the lineup. I'm not too hooked on any one arrangement (Jeter-Ichiro or Ichiro-Jeter), but I think they need to hit 1-2 (I slightly favor Jeter leading off).
There is no way I would have Granderson hitting in any of the 3-4-5 slots. No way am I slotting in a guy who strikes out as often as he does. He's on pace for 200 strike outs. My 3-4-5 would be Cano, Rodriguez, and Teixeira (arranged in any order).
My 6-7-8 would be Granderson-Swisher-Ibanez (arranged in any order) with Martin hitting 9th.
With Rodriguez out, my 3-4 would be Cano, Teixeira (arranged in any order). Swisher bats 5th, Granderson 6th. My 7-8 hitters would be Ibanez-Chavez (arranged in any order) with Martin 9th.
That lineup would send 7 consecutive lefties to the place versus right-handed pitching (with the switch-hitters batting from the left side).