Is there anyway after saving an esp in the C.K. to delete it from inside the C.K itself? Or do you have to close it and open Skyrim to delete it? Then reopen the C.K. to try again.

Just delete the file from the Data directory, through Windows Explorer.

The only issue with this is that just deleting the ESP file leaves any associated scripts hanging around in the data/scripts directory.

Then what is the best way to get rid of a messed up attempt to just start from the beginning?

Uncheck the mod from the Data window in the CS, load Skyrim.esm clean, and make a new mod. esps that aren't checked don't get loaded.