Basic dynamics here to illustrate:
If you lower an object down onto a beam so it just touches but bears no weight, then let go so it rests on the beam, then the bean is exposed to twice the weight of an object. That is doing things very gently, and says nothing about an actual lurch.
Now, consider that ropes' breaking strengths are reduced by perhaps 50% when they are bent over small radii, like in a rappelling device or over a ledge.
So, jostling is bad, and small radii are bad. You need 4x your weight just to break even so far.
Now add UV/thermal degredation and normal wear. Double it again to 8x your weight (still breaking even).
But you don't want to break even -- or break anything else -- so use 16x the weight you will lower. This gives you about twice the strength that may actually be required: a safety factor of 2.
I would use something with a breaking strength of around 16 x 250 lbs = 4000 lbs for myself and a light pack. This can be webbing or small rope, but rope will give more friction, which is good.
That is an absolute minimum. Anything goes wrong and SNAPPO! Don't use paracord unless you really like wheelchairs.
As for a way down, I would forgo the rappeling device and do a Dulfersitz:
http://www.traditionalmountaineering.org/FAQ_Dulfersitz.htm
But it does kind of hurt, and you will want to practice at very, very low heights.
Scott