I'm sure you'll get lots of opinions. Here are some basics on tarps:
Shape: Most tarps for hammocking are either rectangular (e.g. 10'x12') or hexagonal. A variant on these shapes is "diamond shaped" (think square but rigged corner to corner). If you want the ability to close the ends (sorta like doors), you'll want a rectangular tarp or one of its variants (some have extra fabric to make bigger doors).
Material: Silnylon is the most common, the cheapest and widely available. The downside is that it is the heaviest (though still relatively lightweight). Spinnaker fabric is lighter, pricier. Cuben fabric is crazy light and very pricey.
I have an OES MacCat deluxe in Spinnaker fabric, but I've modded it (thanks to 2Q and ZQ for the door mod) to give me the ability to close up the ends when windy/stormy weather appears.
I also have a silnylon Winter Dreams tarp (no longer made) which provides the maximum coverage in colder weather.
"The more I carry the happier I am in camp; the less I carry the happier I am getting there" - Sgt. Rock