I thought that I might as well give a 3rd Badge update. Which, surprisingly enough, I struggled more with Falkner than with Whitney. At any rate... I chose Totodile at the start in order to use it as a cut slave and rushed through the beginning part of the game, quickly catching a Spinarak, Poliwag, and a Gastly right off the bat. I boxed my Totodile at this point and used my Spinarak to beat through Bellsprout tower. After that, I trained the other two on my team slightly. I got lucky, and my (at the time) level 8 Poliwag ended up beating his Pidgeotto. Poliwag then was able to zoom through both Slowpoke Well and Bugsy's gym. My Rival then went down without much effort.
Realizing that none of my team could learn cut, I got out Totodile and taught him cut. After getting through Ilex Forest, I stared at the Pokemon Communication Center and then put Totodile back into its box and then beat through the underground tunnel. Feeling pretty good with my levels at that point, I entered Whitney's gym and slammed through everyone with Poliwag. Whitney's Milktank was quickly finished off by Gastly's Curse and Hypnosis. With that, I grabbed my Plain Badge out of Whitney's shaking hands and saved the game.