The American schools break up for the summer at the end of May, so June is an incredibly busy time. (We have always gone in either April or August and most times it has rained every afternoon. So don't let fear of rain put you off. It may well rain whenever you go. It is a sub-tropical climate, I believe. However fear of crowds might put you off!)
In theory you would be better to wait and go in Sept/Oct, but if it is your honeymoon, then I really think you ought to go on it straight after the wedding. It will just be a holiday if you go months later!
If you go at a busy time, the important thing is to plan your day carefully to avoid queues.Buy the 'Unofficial Guide' and follow his touring plans to the letter and you will not queue for more than a few minutes. Always be there at opening time. It is easy for us Brits to get up early because of the time difference and the parks are pretty empty for the first two hours. Use 'Fastpass' at Disney. Consider staying at a Disney hotel so that you can get early entry to the parks. You can do a lot in that hour before the doors open. (You also get three extra hours in the evening, but that is not so useful because the Americans are awake then so they are all there crowding the place.) Disney hotels have the 'magic' too. The cheapest ones are fine, although the deluxe ones are lovely.
And congratulations on the wedding!
