If you were concerned about ever having to do an impromptu rappel, I would strong suggest that you pack prussic cord of the 6 to 7 mill diameter or a 1/2 inch tubular webbing, and a "SWAT" harness (they are normally just nylon webbing sewn into a seat formation, that can take a multitude of sized people) a figure 8 device, and a set of 4 locking carabineers. While the cost will be about $110 for all of that but it will fit into a pretty small sized pack.
I would go for rope that is a bit thicker, partially because of abrasion concerns but also because in assembling a minimal kit like we are discussing, I want something that is UIAA rated for lead climbing, whatever the diameter might be - currently something around 9mm. You almost are likely to face a situation where climbing up is necessary, as well as rappelling, and you want to be ready for that. I would throw in a couple of slings, and perhaps a small chock or two - it would depend a bit upon the precise situation. As has been pointed out previously, a proper climbing harness is so light these days that it makes sense to include one as well.