Consider the length first. In order to lounge comfortably in a hammock, you need one that is long enough to not clamp your feet together. Unless you have spreader bars that are inserted in the ends to make the hammock rectangular, rather than banana shaped, you'll need one that is at least two feet longer than you are. Add an extra foot or so to allow you to put your arms above your head for true hammock sleeping comfort.
The hammock should be wide enough to accommodate you without excess compression. Part of the pleasure of hammock sleeping may be the feeling of being enclosed. But that can be taken too far. Allow enough material to come up alongside your body, but not to be smothered in a cocoon. If you use spreader bars, the width should be at least several inches wider than you on each side.
Weaving method plays a large role in the comfort of your hammock. Mayan hammocks, for example, are made with a much looser weave than Brazilian hammocks
Material choice is equally important. Among other things, the material affects the amount of stretch. A rope hammock or Mayan hammock
Modern materials have been incorporated into hammocks as they have so many products. But most are still made from cotton or nylon, though Olefin or polyester are available options.
Nylon will generally wear longer and often be more moisture proof. But cotton blends have come a long way. With special treatments they can often handle moisture reasonably well. But unless they're specially treated they can be more subject to mildew over time.
Polyester will weather extremely well, but it usually doesn't produce the most comfortable possible hammock. Still, for occasional use or even (as some hammocks are) just for decoration, they provide a modest-cost alternative. On the other end of the price scale, Olefin is used in some more expensive models. It wears well, cleans easily and can be woven into a very comfortable product.
If you want the least expensive option, a rope hammock
Beyond the basics, taste will dictate your final choice, of course. Hammocks are available in a huge variety of colors and designs and you'll want one that complements your decorating scheme.