We go to Disney every year the last week of May and 1st week of June. It is always hot, and has been rainy the last two years. Last year, it rained every day, some days all day rain. Other years, there is just the occasional afternoon thunderstorm. We always have our ponchos at Disney with us, and just carry them to the parks based on the weather forecast for the day.
As to what to wear, we always were shorts and tshirts. It is too hot for pants, and you will not need a jacket or sweatshirt. It is perfect weather for pool time and water park time.