We went the first week in June last year (our first time too

) and it was fab.
The weather was great, we wore shorts and t-shirts the majority of the time. It drizzled quite a bit, but it wasn't at all a pain, as it was so warm you dried off straight away. We even sat outside in the rain to have cocktails when we returned to the hotel one night
EMH was fantastic and everyday at this time. You will be able to do loads of rides and we managed to get loads of photos of the park with no one else in it
During the week it was quiet during the day - not too long to wait for anything (except Big Thunder Mountain and Crush which could be 30-45 minutes sometimes). We were there Thursday through to Tuesday. Thursday was quiet (and I expect the Wednesday you arrive will be too) but the closer to the weekend the busier it got, with Saturday being absolutely choca block (we gave up and went back to the hotel), but when Monday came round it was really quiet again.
We loved this time of year and would love to go back this year at the same time, but after our January trip we just can't afford it
I'm sure you'll have a great time though. Where are you staying?