Route 1
Required: Eevee

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Viridian Forest
*Do not catch anything that spawns before using the lure, except Pikachu*
Planned: Caterpie (evolve x2), Weedle (evolve x2), Pikachu, Bellsprout
Bonus: Bulbasaur
Notes: The goal for the forest is to get Eevee to Level 10 and to catch the two bugs and a grass type. There are two common ways to achieve this:

No Pikachu Caught: Use the Lure ASAP. Hover under the grass until a glowing Caterpie, Weedle, or Bellsprout is seen. Once one is seen, 1c catch the non-glowing bug, 2c catch the glowing bug, and 2c catch the Bellsprout
Pikachu Caught: Deposit Pikachu and use the Lure ASAP. 1c catch a bug, 2c catch the other bug and 2c catch the Bellsprout

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Route 2 North:
Planned: Caterpie (evolve x2), Weedle (evolve x2), Pikachu, Bellsprout
Notes: Things come in at Level 9 with a Lure rather than Level 7 in the forest. If you need EXP for Level 10 on Eevee, this is a good place to get it

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Route 3
Bonus: Charmander, Ekans

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Route 4 (Center)
Planned: Magikarp

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Mt. Moon
*Do not catch anything that spawns before using the lure*
Planned: Clefairy, Paras
Situational: Geodude
Last resort: Clefable, Chansey
Notes: Don't catch anything before using the Lure. Catch glowing Geodude under Lure for a nice EXP Boost. Ignore Geodude otherwise. Catch Clefable and/or Chansey at your own risk

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Route 4
Planned: Psyduck
Bonus: Charmander, Ekans
Last Resort: Rattata
Notes: Psyduck is a planned catch, but can appear in 3 more places later so leaving without it is okay. If you are close to Level 15, consider catching Rattata and catching a Raticate later

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Route 25
Planned: Psyduck
Bonus: Squirtle, Venonat, Meowth
Notes: Psyduck is a planned catch, but can appear in 2 more places later so leaving without it is okay. Squirtle can evolve if you want the extra Pokemon

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Route 5
Planned: Vulpix (evolve), Jigglypuff (evolve)
Bonus: Abra (evolve)
Notes: Running through the grass here is optional as the same encounters appear on Route 6

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Route 6
Planned: Pidgey (evolve x1), Vulpix (evolve), Jigglypuff (evolve), Psyduck
Bonus: Abra (evolve)
Okay: Rattata (evolve)
Notes: Everything here can be obtained later (risky!) if you get bad spawn luck. Catching a Lured Rattata here is okay as it will evolve in 3 levels

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Route 9
Planned: Rattata (evolve), Spearow (evolve), Nidoran f (evolve x1), Nidoran m (evolve x1)
Situational: Raticate
Notes: Everything here also spawns on Route 10. Catch Raticate here if you caught a non-evolvable Rattata earlier

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Route 10
Planned: Rattata (evolve), Spearow (evolve), Nidoran f (evolve x1), Nidoran m (evolve x1)
Bonus: Krabby (evolve)
Situational: Raticate
Notes: Catch Raticate here if you caught a non-evolvable Rattata earlier

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Rock Tunnel
Highly desired: Rhyhorn
Planned: Zubat (evolve), Machop (evolve), Geodude (evolve), Cubone (evolve)
Situational: Graveler
Bonus: Charmander (evolve)
Notes: Catch Graveler if you got a Geodude earlier

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Route 7 & 8
Planned: Vulpix (evolve), Jigglypuff (evolve)
Bonus: Abra (evolve)
Notes: Usually nothing left to catch when you get here, but it can be a good backup

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Lavender Tower
Planned: Gastly (evolve)

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Route 16 & 17
Required: Ponyta (candy evolve), Doduo (evolve)
Planned: Pidgey (evolve x1-2), Rattata (evolve), Psyduck (evolve)
Notes: If you still need Rattata or Psyduck, catching one here allows it to evolve. Candy Rapidash as soon as you get it

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Route 21
Required: Staryu (evolve)
Planned: Tentacool (evolve)
Notes: You cannot use 2c catching in the water

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Mansion
Planned: Koffing (evolve)

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Last Resorts:
Weepinbell or Tangela on Route 21 grass. Magmar in Mansion. Diglett after Lt. Surge in Diglett's Cave, Moon Stone evolution by getting extra Moon Stone after Sabrina