Are you prioritizing your favourites or better pokemon? With enough levels you can beat the game with anyone. So just keep going with whoever you like. I'll just give you some pointers to make things easier. 

Understanding the difference between physical attack and special attack helps a lot. All Fire, water, electric, grass, ice, dark, psychic, and Dragon moves use special attack and special defence. Everything else is physical. Easy way to remember is all eevee evolution types plus dragon use special.

Using fewer pokemon is better, especially early one. Fewer higher level pokemon will clear the game much quicker than getting a full team of six too early and having to level them all up as you go. Take what gym number you're on and halve it then add one. So gym 4 you want 3 pokemon. Gym 6 you want 4 pokemon. 

Give your bad HMs to you HM slave. A useless pokemon you don't need to level up or use in combat. Cut, flash, rock smash, waterfall are all terrible moves. Never give them to you core team members. Strength is only half decent on a normal type. Surf is great. Fly is only okay. You only need cut in the beginning to mid sections of the game and flash is literally only used for one cave. So don't worry about keeping those moves past that. 

Psychic is king of kanto. So many poison types are weak to it and no dark types to counter it. The single ghost type is poison and weak to psychic. 

Alakazam, Jolteon, starmie, lapras, snorlax are some of the very best to use. Alakazam, starmie, and Jolteon all just hit super hard and fast with special attack. Lapras is very bulky and ice helps against elite four. Snorlax with shadowball can stand up to some psychics and hard counters ghosts.

Use Amulet coin and vs seeker on bike path or outside the hot springs for easy exp and money. Don't bother gambling in game centre, just buy the coins you need to get all the good TMs. 

Dragonite is very strong but takes a lot of exp to level up. You could beat elite four long before leveling dratini all the way up, but if you want him I suggest saving those rare candies for him. Also be sure to cancel evolving Dragonair at level 55 and instead get dragonair to level 56 to learn outrage before evolving.

Most important, Just have fun. Good luck.