Greetings. This is a guide on how to bust this game open wide without any external software, from the starter pick.
Note : expect to have to savescum *a lot*. It's worth it.
So, starter choice is Bulbasaur, and get the balls. Then, save and start moving.
Your goal is Cerulean : go north until Pewter, then east through Mt Moon until you reach Cerulean. Save after every screen transition so you can flee / quit and reload quickly in case of annoying randoms / Rocket grunts.
Sleep to night, then go north once. This is the first big RNG moment - your objective is to catch a Gloom. So, a thing to note is that the Pokémons on the screen only change upon entering / clicking the circling arrow button.
So, the idea is to reroll until you find a Gloom on the screen. It's somewhat rare, so hang in there. Once a Gloom is on the encounter selection screen, save, and now that Gloom will stay here after reloading, so you essentially have infinite catch attempts. It is always l21.
Catch the Gloom by throwing balls at it. Don't bother damaging it. Bulbasaur is optimal becasue it resists Mega Drain. If you die, reload.
You'll also need a Venonat. You can catch it now on the same Route, or on a later Route if you prefer (it will be at a higher level).
If you're low on money and balls, you start with an Everstone you can sell, and you can grind cash on the Geodudes in Mt Moon, as well as Brock when you have Gloom.
Once Gloom has been obtained, heal if its Mega Drain PP is low. Then, pulverize Misty with Mega Drain spam and zero hesitation. Save before her if things go south. You'll get a fishing rod for this.
Now, save, heal, and go south of Cerulean. You'll be promptly mugged by the Rocket trio from the anime - take down Meowth, then Ekans, then Koffing with Mega Drain spam. You'll arrive on Saffron. As before, remember to save after moving every screen.
Go East until Lavender, buy balls if needed, then go south once. Here, you can fish for various Pokemons. Your objective is Tentacool. Depending on its level, Bulbasaur might be more suited to weakening it. Use your judgment here.
With Tentacool caught, back to Lavender. If you didn't pick up Venonat earlier, you can find it at night around the routes south of Route 12 you just caught that Tentacool on. It'll be up to level 30.
There's a few more Pokémons you can choose to grab in the area around Fuschia, like Magnemite during the day (it's got Thunder Wave for catching and quad flying resist is handy), or Noctowl during the night (early Fly bot)
That said, your next goal is to go to Johto as quickly as possible, for which you need 500 bucks. There's a swimmer somewhere south of Fuschia during the day - you can beat her up for money alongside the wilds.
Geodudes remain a convenient source, as well, Brock if you didn't fight him before, and you can catch Murkrow at night west of Celadon for beating up wild psychics. (not Sabrina tho, unless you evolve it and put quite a few levels in it. A quick sidenote : Stone evolutions don't deny you levelup moves in this, at least for Honchkrow)
Once you have that money, go to Saffron and pay the fare to Goldenrod. We need even more money, but we have a convenient source not far. Go north of Goldenrod, then maneuver to Violet City - use the map to direct yourself here.
Once in Violet, go east into the Dark Cave, saving if necessary. Venonat was necessary here for Flash. First, the Gravelers here are an excellent source of money thanks to Gloom. You can evolve it if you desire, but it's unnecessary.
That said, the big thing we're looking for is through the east exit - you can find wild Gligars here. Catch one. You can evolve it as well with a Razor Fang, but it's unnecessary. Be careful to keep Poison Sting on it.
Now, fill up your party to 6 if it is not full. The Pokémons are irrelevant. Also note you'll need more money here - you need to grab around 6-7 Pokéballs *after* filling up your party and the fare to return to Kanto (which is 500 as well). If you have a Murkrow / Honchkrow at a good level, you might be able to handle Morty for money.
There's Miltank and Tauros in the day, around the west of Ecruteak if you want a Strength bot. You won't need it right now, however. Gligar handles cutting ability.
Once back to Kanto and your team is filled up, put Gligar in front of your party. Go back to Cerulean, and sleep to day. Go east, then into the Power Plant. You need Surf, hence the Tentacool.
And there's a Zapdos here, at level *55*. And we're going to catch it. Save on the Battle / Pass screen. Here is the basic flowchart for the fight :
Gligar uses Poison Sting until Zapdos gets Poisoned. If Gligar dies before, reset.
Once poisoned, Gligar spams quick attack until Gligar dies or Zapdos is around half HP.
Then, throw balls until it stays, quit the game and reload the save if you wipe.
Once you caught it, congratulations ! You've basically won thanks to the level advantage. Get Erika and Janine's badges first because they're the easiest for your new superweapon. You can also return to Johto and give Falkner and Bugsy what-for. Chuck as well, but be a little careful with him - his Pokémons are very high-leveled.
Careful of Jasmine, she has a Steelix that can be a pain to deal with for Zapdos, and her Magnetons can be a nuisance.
If you want more birds, there's Articuno in the Ice Path east of Mahogany (l55, need Strength), Lugia south of Olivine and Ho-Oh at Ecruteak Bell Tower (both l65 with recover, so good luck.).