I live pretty close to Zion and can help out a little. The park will have people in it in Sept, that is the prime time for climbers and Europeans. Sept and early Oct are quite busy, you won't be lonely. It will be hot, 90s for sure. bring plenty of water and Gatorade.
You'll be able to camp right inside the park or there are a few areas 5 miles outside that allow free camping. Coal Pits Wash is one. If you plan on camping in the backcountry you'll need a permit. I don't think it will be difficult to get one.
Angel's Landing, is spectaculer but will require at least 4 hours. I know it would take me at least 5 and I'm in fair shape. You could leave a pack at Scout's Lookout and go out onto Angel's, just close it to keep out the marauding chipmunks!
Tim is right about the Sunrise, but it's behind the Museum. This is accesible by car all year and the picture will be awesome.
Consider doing the hike in the Narrows, I did it mid-Sept a couple of years ago. The water was warm and not very deep. You just hike upstream as far as you like. Narrows Outfitters out side the entrance does boot and walking stick rentals. You will want a hiking stick of some sort.
Emerald Pools is a nice hike but there may not be much water this time of year. If you get lucky enough to get a shower it would be nice hike. Hidden Canyon is a good morning hike as you'll be shaded, pretty good views and shorter than Angel's Landing.
Please take the time to drive up thru the tunnel to the East side. This is my favorite area and there are some really nice washes to hike in. There is a short hike by the large tunnel, Canyon Overlook, pretty easy with a spectacular view. Good photo op in the AM, it will wash out a little in the afternoon.
Please drop me note if you have any specific questions. [email protected]