The last 2 yrs we have gone the second week of June. This yr we are going the first week for a change. The crowds on the second week slowly pick up through the week. You shouldn't have to worry about the Gay Day crowds at Mk because i believe that event ends on the 9th. The crowds aren't bad accept at closing time at Mk with the fireworks and parade. I think everyone from Orlando desends on this park at closing. We used FP for some rides like Buzz,and BTMR.
Have a great time!