>>33124989Also, you can technically break the sequence with the thirsty guards by transferring a drink from Stadium 2 so that you can access Saffron City immediately after getting the Ship Ticket from Bill and heading south of Cerulean City. From there, the world is your oyster for the most part.
Go north to go back to Cerulean City and beat Misty.
Go west to go to Celadon City where you can get an Eevee, do the Game Corner, enter the Rocket Hideout, and challenge Erika (requires beating Misty and getting HM01 first). You won't be able to get far on Route 16 though because of Snorlax.
Go east to go to Lavender Town. Going south from there to Route 12 leads to another Snorlax roadblock, but you can always clear most of Pokémon Tower and even rescue Mr. Fuji and get the Poké Flute if you've cleared Team Rocket in Celadon.
Go south to go to Vermilion City, challenge Lt. Surge (requires Cut or Surf) and do stuff there.
But it's completely reasonable to go
>Cerulean City>Route 5>Saffron City>Route 7>Celadon City>Rocket Hideout - Beat Giovanni>Celadon City>Route 7>Saffron City - Beat Giovanni, then Sabrina (anytime from this point on)>Route 8>Lavender Town - Save Mr. Fuji>Route 12 - Snorlax>Route 13>Route 14>Route 15>Fuchsia City>Safari Zone>Fuchsia City - Beat Koga>Route 19>Route 20>Seafoam Islands>Route 20>Cinnabar Island>Pokémon Mansion>Cinnabar Island - Beat Blaine>Vermilion City - Beat Lt. Surge and find Cut>Cerulean City - Beat Misty>Celadon City - Beat Erika>Viridian City - Beat GiovanniWhile Brock will always be first and Giovanni last, Misty can be as early as 2nd and as late as 6th, Sabrina as early as 2nd and as late as 7th, Koga as early as 2nd and as late as 6th, Blaine as early as 3rd and as late as 7th, Sabrina as early as 3rd and as late as 7th, and Lt. Surge as early as 3rd and as late as 7th.