With the REI provision, a Hennessy Ultralite Backpacker Asym Zip would be a great start. Any of the Hennessy models will work, but get a zip model.
http://www.rei.com/product/814263/hennessy-hammock-ultralite-backpacker-asym-zip-hammock
I recommend changing the suspension ropes to whoopie slings and you will aslo want longer tree straps and carabiners, but it will work as sold.
Include budget for a bottom insulation system:
Wide foam pad (cheapest and lightest, but least comfortable)
Hennessy SuperShelter system (light and easy to use— for summer)
Underquilt (best results for 3-season but most expensive)
Tarps tent to be larger than UL backpacking models. a 10'x12' tarp is not unusual. Hennessy's diamond fly is okay for good summer weather, but a large tarp will provide more protection. Add that to the budget with the insulation.
If not Hennessy, then look at the Warbonnet Blackbird
http://www.warbonnetoutdoors.com/blackbird/
Note that I recommend hammocks with integrated bug nets– the only way to fly if you need bug protection. Otherwise, you can go with simpler plain fabric hammocks like the Warbonnet Traveler.
Be prepared to spend some time experimenting with hanging the hammock. Small changes in length and angles can make a big difference in comfort. If you plan on learning at the campsite, you may not be happy with the results. I put a couple posts in the back yard so I could experiment and sleep as many nights as I wanted to learn the tricks. It's not difficult once you understand the principles, but it isn't a 15 minute process.
A cheap hammock will be as miserable as a cheap tent or any other cheap gear. With experience and tweaking you can get any hammock to a workable state, but you end up nickle and diming yourself. The hammock body is the cheapest part of the setup: you need to add suspension, insulation and tarp to make a workable system. A $15 hammock is okay for a nap, but not for camping in North America.
If you sew, it is an easy project to make a basic hammock.
And there is a hammck forum here too :)
http://www.backpackinglight.com/cgi-bin/backpackinglight/forums/display_forum.html?forum=66