3mm climbing accessory cord will do the job nicely, you can go thinner with a dyneema line or chunkier with some 550 but it's a bit overkill. I'm using 2mm Exped stuff at the moment which is nice and compact.
A useful length is 10m so you don't have to be too picky with the trees, if you're hammocking and restricted buy your suspension then as short as 7-8m is usually enough. Personally I like the extra length.
EDIT:
Meant to say, another option is just to tie a shorter length to each end of the tarp rather than having one long continuous piece, the only downsides with this is you don't have the added protection from falling branches in wind, or sometimes it can be hard to avoid sag with the bigger heavier tarps. For lightweight PU nylon or silnylon it's not too much of an issue.