Rope???? If it's on a sailboat, it's called a "line".
For the righting line, the best stuff to use is called "hollow braid". It's soft, large diameter, and you can slide bungee cord inside it to make your righting line snap back. It's available through Murrays...
For tramp lacing, any low stretch, high quality line will do. I prefer to use New England Ropes Sta-Set line as it is inexpensive, good quality, and available a West Marine. 1/4" diameter is a good size for tramp lacing.
Don't purchase line from Home Depot, it's garbage and not something you would want to use on a boat.