After reading through the Hammocks forum on Bushcraft USA, and product reviews on Amazon.com, I ordered a Grand Trunk Skeeter Beater hammock. It's nicely made with a polyester taffetta body and a zip-open bug net sewn to it. There are S-hooks attached to each end, and it comes with two cords to hang it, along with some smaller diamter cord to hang the netting. There's also a sewn-on stuff sack for storage. The hang cords aren't very long and in some places you're not supposed to use rope to hang hammocks because they can damage tree bark. So, I also ordered a set of Hammock Bliss extra long tree straps. The webbing straps don't dig into tree bark like rope, and will allow me to hang the hammock between trees that are further apart.
In case of rain or squirrel poop, I'm planning to rig a tarp over me as a fly. For now, I have a cheap camo poly tarp. Assuming that I like hammocking, I'll probably get a lighter nylon tarp like an Etowah or one of the tarps from the BCUSA store.
To prevent getting bitten by bugs through the hammock, I plan on spraying it down with a permethrin-based bug repellent before taking it into the woods. I normally use DEET-based sprays but it's my understanding that DEET can damage polyester, and the last thing I need is for it to dump me on the ground.
I plan on trying the hammock on the first trip and will post a follow up after I get back.