I carry and use a net hammock...depending on how I feel, either a two man or a one man. I have used ones with spreader bars and without. I recommend spreader bars for the one man. I bought these hammocks from Wal-Mart or K-Mart for 15-30 dollars.
In terms of carrying it, they do fold down small and are light. My hammocks actually travel everywhere with me, whether it is in the city or on the trail, it is quick to put up and pull down, leaving very little sign that I was there. It is great for those afternoon naps at the park, with a book and a bottle of lemonade.
Some tips and tricks:
1: ALWAYS make sure the tree is alive. I learned this from first hand experience, when the tree fell, almost crushing me.
2: I use a painters drop sheet as a tent, carrying some 550 cord to put over the top. In the summer, you can open up the sides to let a breeze in, and in cooler weather, you can drop it for a greenhouse effect. It works great for blocking the wind as well. Use rocks or dirt on one side to keep out any rain on the uphill side, to prevent rain from flowing under you. It stays nice and toasty.
3: If you do use a painters drop sheet or a tarp, make sure you don't place it above a hornets nest. I did, and it wasn't fun. I didn't get stung since I was above the nest, but it was an eye opener seeing them flying around my hammock the next morning. Fortunately I was able to move the drop sheet and free them without them getting upset with me.
4: You will stay cool in a hammock. If coolness is a concern for you, move the hammock low to the ground and pack clean leaves and other detritus around. It will keep you insulated quite well.
5: If you aren't in bear country, you can hang your bag on the 550 cord under the painters tarp. It is convenient to retrieve things without leaving the warmth and shelter of your tarp.
6: I use carabiners to suspend possibles above my hammock on the 550 cord. Possibles include a flashlight, and sheathed fixed blade knife, and a water bottle. These hang above my head and chest, for easy finding. Quite convenient, if you ask me.
7: If it rains, you want to keep the rain from entering via the ropes suspending your hammock and tarp. Tie a small knot and it will trap the water trying to drip in and redirect it to the ground.