You picked a great time frame. Can't ever predict the weather, but on average first half of June sees the most summits as I remember.
Bring a pee bottle. Flexible nalgene works well. (learn to use it before the trip)
Mountain House is great for high camps. I like Chicken a la king a lot. There is mashed potatoes with grilled chicken breast which is good too. In the morning I like granola with strawberries (by some other freeze dried food company).
Make moving to 14K your #1 priority. Even if weather sucks still do your best to move through it lower on the mountain (as long as avalance danger is low and it is reasonable). There is nothing worse than being stuck somewhere bellow 12k for several days. To summit you need to acclimate at 14k.
Pick good partners.
I think I will write an entry on my blog with many more tips about that climb. Some people might find it useful...