You don't necessarily have to go with an eye sling. I just use a single length of 5/8" double esterlon. I double it over, and that forms the eye, then both ends go round the tree, and back with a timber hitch. Doubled rope gives you double strength, or near enough to. Mine is 45', which gives 22.5 feet doubled, which gives a diameter of roughly 6' plus enough to go back round half way again for the timber hitch. If you are going for a single rope eye sling then go for around 20'. 15' is really only good for trees up to about 3' diameter. If you are getting a couple, or already have one then 12' and 20' is a good combo. Small trees you can just use a normal sling, bigger trees you can just use one of your lowering ropes to attach the porty.
Make sure you get a color that is different from your climbing and lowering ropes.
Shaun