I have not camped while flying, but I do a bit of hiking, and thought I´d share my experiences with different types of shelter.
First of all, hammocks are out. Nice and fun near a road or something, but when you add a bug net and a tarp in addition to the fact that you MUST have two stout trees, then it will quickly become relatively heavy and it is a lot of faff to erect.
Tarps are not bad, but you need a bug net and something to hold it up. I would imagine that it would be easy to use a wing. I have chosen tarp over tent sometimes when I either use trekking poles (rare) or know for sure I am camping below the tree line. Don´t need as stout trees as for a hammock.
Tents are the best. I love my MSR Access. It is self standing, and I can erect only the inner tent when it is warm and I need to keep bugs out, or both the inner and the outer when it rains and snow. It is sturdy enough for limited winter use, but get the newer version with the extra vent high up. I slept in a heavy snowfall once, and the ventilation along the bottom got completely covered. Woke up in the middle of the night, confused as shit and with the worst headache I have ever had and felt like I was choking. Tore up the zip to get out and get some fresh air… So I have had my sent to a specialist to put two extra vents on it. The Access is really, really light too by the way.
The ideal setup, and in my opinion also worth the weight penalty, is a decent tent that is self standing and where you can erect only the inner tent - AND a tarp. On days when the sun is really beating down, the trick is to use the tarp to cast a shadow over your tent. It will be airy enough to not get that horrible greenhouse effect where you just get baked inside, and actually stay somewhat cool. If the inner tent has good enough ventilation ofcourse.
For sleeping, it depends. If you are very careful, an inflatable sleeping pad is king. If you can sleep in a little discomfort, a closed cell pad just cant get ruined. They are light, but take up a lot of space. You need two on top of each other when it gets cold. Most people dont know you will loose more heat to the ground when camping, than to the air. And ofcourse a sleeping bag. A liner is good. I think that cotton is the most comfy, but does not add a lot of warmth. It can also hold moisture, wich is bad and kills all insulating properties. Silk is the «best». Light weight, insulated very well for its weight, and will not loose insulating properties when wet. (but always feels wet), and a synthetic fleece is the warmest, but very heavy. A pillow can be nice.
Sleeping outside is a matter of training. You can build up tolerance for sleeping on the hard ground with nothing than an inch of closed cell foam underneath you. If you sleep outside somewhat sporadic, don´t think you are cheating or being a sissy or anything like that because you get a nice pad and a cot. A good nights sleep is everything. It is important when hiking, and if you are flying the day after then you absolutely need to be well rested. The one thing I usually bring to spoil myself when hiking, is a big, fat, warm sleeping pad