Static climbing or arborists rope, of nylon braid (technically a kermantle), would be the best of what's easily obtainable. I'd probably use 10mm, or something close to it, to avoid it cutting into your neck. If that isn't a problem, I might go as small as 7mm. The same size rope from a supplier for sailboats would also work well (go with a nylon braid, ideally indended for use in halyards), and it is almost always available by the foot from boat supply stores, where climbing and arborist suppliers often only sell rope by the (expensive) fixed length.
Honestly, in such short lengths as people would be using for partial, whether it's static or dynamic doesn't make much difference. Stretch is a percentage of length --meaning a 1% elongation of a 100m rope would be 1m, but the same elongation of a 3m length hung over the top of a door would only be 3cm. Slumping 3cm lower is a negligible factor to compensate for.
The critical element of any rope choice is its working strength, and there are 12mm ropes that will break under my weight and 4mm ropes you couldn't break with four people hanging from them. Sometimes abbreviated "SWL" (Safe Working Load), you need this number to have any assurance it won't break. Obviously, SWL needs to be at least as much as you weigh. Don't try and split hairs by saying, "I can use a weaker rope because part of my weight will be on the floor." A knot --any knot-- or a hard turn in the rope --such as over the top of a door-- creates a place where stresses accumulate and effectively weakens the rope, so the bottom line is that you need a SWL at least as much as you weigh.
As a rigger on boats, I could give all sorts of ideal technical advice, with ropes of all sorts of fantastic, space-age materials that are high-strength and low friction, but the details would probably make everyone's eyes roll back in their heads.
