Double hammocks are great for cuddling and looking at the night sky, but crap for sleeping. I would get separate hammocks for sleeping.
I use an eno hammock, there are a lot a nicer hammocks out there, but I have never felt the need to upgrade. The separate rain fly, bug net, and hammock, give more options, and don't take much longer to set up. If its not forecast to rain, and looks like the forecast is accurate, I forgo the rain fly. If the bugs aren't bothering me, I forgo the bug net, etc.
Kelty makes a hammock tent that is compatable with any camping style hammock that can be set up open like a big rain fly, or put into storm mode where it envelopes you and your hammock. I'm sure other makers have similar options.
Personally, I carry and use several nylon backpackers tarps I bought at Walmart for like $7 each, and set them depending on the situation as wind breaks, rain fly, double layer rain fly, etc.
A gear sling is something I have debated getting. It is basically a little hammock that suspends your gear under your hammock, keeping it off the ground, and within reach.
Get the tree friendly straps. They are simpler to use than tying ropes, and on most state and national forest lands they are required.
A link to a hammock comparison and review:
http://m.outdoorgearlab.com/Hammock-Reviews