July is by far the busiest, and usually when the June grasses come in (seaweed). Anytime there is a lot of seaweed, you get more jellyfish and other types of marine life. Also the MS bar hosts its annual summer conference at Sandestin in July (generally the first 2 weeks) so it is really packed then. I'd say go early or late as possible, the first weeks of June are amazing in my opinion, and not nearly has stiflingly hot as August will be (but if you have to do August, the worst of the crowds and seaweed should be gone then too).
Also if you aren't into the big resort feel (Sandestin), look for condos on Okaloosa island. It is the barrier island off the coast near Destin, much less crowded, still plenty to do, less 'high rise' and more 'low rise'. Also would save an hour or two driving if you're coming from the west.
And don't let the seaweed/jelly idea freak you out, you can usually wait them out (they'll come and go in a day or two) or do something else on those days, it is not really any different than a chance of rain. I just wanted to mention it so you'd be sure to have pool access for any little ones on those days. I just moved from the gulf coast & we went to the beach frequently, feel free to PM me with other questions, suggestions, etc.
re: resevations, you can also sign up for Sandestin's emails & get specials they don't advertise & you can find good deals on Okaloosa island and in Sandestin on vrbo.com