What type of compression fitting do I need?
You don't need the compression nut. With that water hose, you should connect it directly to your water supply shutoff valve.

The compression nut is used when you have a copper pipe as your water supply, like this:



If that's what you have, remove the nut and the copper pipe. Your braided pipe connects to the water supply like this:



And connects to your dishwasher like this:



Use the teflon tape ONLY on the threads between the elbow and the dishwasher. The braided hose has a gasket so DO NOT use teflon tape on those threads.