I like spending my first night at Horseshoe Meadows. The last night should be at the trail head, since you need to get up super early for a day hike. You don't want to do the extra one-hour drive from HM to WP before the hike.
I bought a cot for the car-camping part, and found that it really beats sleeping completely on the ground.
Regarding food: Make sure you eat most on the way up. If AMS kills your appetite, you'll end up carrying it home. So eat it early, before the appetite leaves.
I think you can see the consensus on sleeping in Lone Pine. Save that for after the hike.
