So you're starter is gonna be Cyndaquill it helps early on with Bugsy and it as a Typhlosion works against Jasmine and Chucks Poliwrath with thunder punch, Pryce's Piloswine, Koga's bug types in the elite 4, Karen's Murkrow with Thunder Punch, Lance's team since they all have part flying, Lt. Surge with Earthquake, Erika, Blaine with Earthquake, Janine's Ariados and Venomoth, Blue's Pidgeot and Gyarados with Thunder Punch, his Exeggutor, his Arcanine with Earthquake, Red's Pikachu with Earthquake, his Venusaur, and his Charizard and Blastoise with thunder punch. For it's moveset, Flamethrower for STAB (Obtained in Game Corner for 5,500 Coins), An alternative for Flamethrower if you do not wanna grind at the game corner is Fire Punch which is at the goldenrod department store. Earthquake is in victory road and is for coverage. Strength for HM usage and a strong filler attack, you get it from a sailor in Olivine. And finally Thunder Punch for coverage and it is also obtained at the department store.
Geodude can be found earliest at route 46 right above route 29, The Geodude line does well against Falkner and Bugsy early on (If you level up your Geodude to know Rock Throw), Morty's Poison types, Jasmine, Pryce's Dewgong (But that's risky), Koga, Karen's Gengar (And Vileplume but that's risky), Lt. Surge, Lance's Team except be careful with Gyarados, Blue's Arcanine, Pidgeot, and Gyarados but also be careful, Red's Pikachu, and his Charizard. His moveset consists of Earthquake for STAB (Level 41), use Dig earlier on, Rock Slide if you breed Any of the Geodude line with Sudowoodo, or Rollout which is learned at level 34, Explosion to put huge dents in peoples teams, and then either Headbutt or Protect depending on if you want a filler attack spot or a move that can prevent you from taking damage, I recommend Protect though.
Spearow can be found on route 29 at the earliest and its line does well against Bugsy, Chuck, Will's Exeggutor, Koga's bug types, Bruno's team except Onix, Karen's Vileplume, Erika, Janine's bug types, Blue's Exeggutor, and Red's Venusaur. So Fearow isn't the best member of our team but early on as a Spearow he still can deal with various trainers like bug catchers and lasses, his final moveset will have Drill Peck for STAB (Learned at level 40) Fly because it is an HM that we need and if you run out of PP for Drill Peck, Return for a filler attack you can replace it with Swift or Double Edge if you want but I prefer Return, and Agility to raise your speed.
Bellsprout can be found very early on route 31, and the line does well against Chuck's Poliwrath, Pryce's Seel and Piloswine (But that's risky), Brock, Misty but her Lapras is risky, Erika with Sludge Bomb, Blue's Gyarados and Exeggutor, and Red's Blastoise. Now his moveset is Razor Leaf for STAB (Weepinbell learns it at level 27), and Sludge Bomb for STAB (Found in the area near the Lake of Rage), Sleep Powder to for making other Pokemon fall asleep. And then Growth to raise your Attack and Special Attack stats.
Umbreon can be obtained if you level up Eevee with high friendship at night, Eevee can be gotten from Goldenrod City. The only reason it is on the team is coverage for Psychic and Ghost Types but if you want you can use Gengar or Heracross for Psychic types. It will do well against Morty, Pryce's Piloswine with Iron Tail, Will's Team, Bruno's Onix with Iron Tail, Karen's Gengar, Brock's Rock/Ground types with Iron Tail, Misty's Starmie, Sabrina's Team, Blue's Exeggutor and Alakazam, Blue's Rhydon with Iron Tail, and Red's Espeon. His moveset will be Feint Attack for STAB (Learned at level 37), Confuse Ray to confuse other Pokemon (Learned at level 30), Iron Tail for coverage, and Swift (Found in Union Cave) because it always hits and is a filler spot (Also because I can't think of a final spot). Not the best moveset but again, he is only for Psychic and Ghost types.
Lapras is found in Union Cave and is a very good bulky water/Ice type. Lapras does well against Jasmine's Steelix, Pryce's Piloswine, Will's Xatu, Koga's Crobat, Bruno's Onix, Karen's Vileplume, Lance's Team, Brock's Rock/Ground types, Erika's Team (But that's risky), Janine's Crobat, Blaine, Blue's Pidgeot, Rhydon, and his Exeggutor with Ice Beam but that's risky, then finally Red's Charizard and his Venusaur with Ice beam but again I wouldn't recommend it. Surf is for STAB and for HM Usage (Found in the Ecruteak City Dance Theater), Ice Beam is also for STAB and is learned at level 36. Rest is to recover health and is found in the Ice Path, and finally Confuse Ray which is learned at level 22.
You can use this team in Gold, Silver or Crystal because their is no version exclusives! :)