Here's a couple suggestions I have about camping on the Willow. The first is to make sure you get there early if you plan on camping out during a holiday or the opening fishing weekend, as the remote campsites fill up quickly on these weekends considering they are free. You might also want to strongly consider a trip earlier in the summer to avoid horseflies and low water levels. Last year there was a lot of wood ticks, so you'll want to be prepared as best you can in case this happens again. The campsites have fire pits, and sometimes DNR staff will stock wood to burn by the shore - which can also help you locate a spot. Take a Willow map showing campsites (as the site you want might be filled) and stick to one shoreline if its your first time on the water - the sites can be tricky to find and are only marked with a small sign. Outside bathroom facilities are available at each campsite, but make sure not to forget toilet paper, otherwise you'll be coming off the Willow missing a sleeve. Practice no-trace camping procedures so the next person to use the site has the same enjoyment you had while visiting.
I'd strongly recommend taking along some beach chairs, as the shoreline is mostly sand, and an evening spent with your toes buried while watching the sun set is a truly priceless experience - try to secure a campsite that has a good view. There's also no light pollution, so star gazing can be amazing on a dark and clear night.
If you plan on doing any fishing take along Gulp bait instead of live bait, as it has produced fish for me and will last much longer if you plan on being out for an extended period of time. A lot of people also troll out here.
These are just a few suggestions that come to the top of my head that can make your trip more enjoyable. There's also a modern campsite on the north end in case you don't plan to stay at the remote sites.
If I don't recall, I also had reception through Alltel the last time I was out on the Willow. My final suggestions is to leave your phone off at all times, but have it along in case you run into an emergency.