First thing I'd like to say is that Dugtrio is a surprisingly useful pokemon. Dig as soon as you get it (even as a Diglett), and the only training it really needs is to go through is Vermillion's Gym. Also, Gen I crit mechanics combined with Slash and blistering speed could prove to be useful, critting everything in sight that doesn't resist Normal, and those can be taken care of with Earthquake and Rock Slide (the latter he gets via TM).
I'm happy to test this out if nobody else has the time. With a moveset of Slash/EQ/Rock Slide/Filler, Dugtrio can potentially take out:
Lt Surge's gym
Erika's gym (speed+slash?)
Sabrina's gym (high speed, Slash and pokemon's low defences)
Blaine's gym (EQ/Dig)
A few of Giovanni's pokemon
4/5 of Lorelei's pokemon with SE Rock Slide, maybe Slowbro with Slash
Brock's Onixes with EQ/Dig, others with Slash maybe
Agatha with Rock Slide for Golbat, rest with Dig/EQ
Dragonite/Aerodactyl/Gyarados with Rock Slide
Pidgeot/Gyarados/Arcanine/Alakazam with various moves
I know there are other pokemon that could defeat all these people, just wanted to highlight this under-appreciated pokemon's usefullness.
Good idea :D Using Bulbasaur or Squirtle until you get it, and then solo with critter () or going duo with starter and dugtio Starter is up to own preference: Blastoise has better coverage, while Venusaur has better special and razor leaf.