Everyone's style choice is different so your length of bottoms will depend on you!
For daytime parks, I like shorts and a tank or short sleeved shirt with walking sandals (tevas.) Since we go back to the resort for an afternoon swim, I always change my outfit for the evening as it gives the daytime outfit a chance to air out so I can wear it another day
For evenings, I wear a bit nicer shorts/top and my nicer sandals (black danskos.) I will sometimes wear a short skirt in the evening (with boy short undies) or even a nice long summer swishy skirt that is cool feeling and not heavy.
I personally am short...er
so I prefer shorter length shorts as long ones make me look squat. I suggest you bring shorts that you do NOT need a belt and are also comfortable, and have pockets (for napkins to wipe the sweat off your brow.) For me, that means cotton shorts with a "band" (elastic but not gathered so if it shows, it is smooth) or cotton/spandex shorts that don't need a belt even if they zip/button on the front. Anything too tight on your waist is not only uncomfortable but also makes you sweat! So I also suggest nothing too high-waisted and in colors that won't show dirt or smudges and that can be worn a couple of times - like light denim colored or light patterns or darker colors (but these can attract heat so beware).
As for tops, make sure you don't have to fiddle with them to keep your bra covered but you don't want them so tight that it restricts airflow and then your sweat shows through. Sometimes taking your shirt and waving it against yourself can make a world of difference in the summer
But my best suggestion is to go early and late to the parks and in the blistering heat, go to the pool, the watermarks, or indoor attractions!