Analysis of current party members:
Mankey is a Fighting Pokemon that specializes in hitting hard and quickly with Physical attacks. It evolves into Primeape at level 28, or the mid-game. As a Primeape, it is similarly built, only more so. Throughout the game, Mankey/Primeape relies upon Low Kick as its only regular Fighting Attack, although it can also learn the powerful Karate Chop and Fury Swipes. This lack of powerful attacks ultimately leaves it limited. Worse, its defenses are poor, especially against Special Attacks. Therefore, although Mankey is useful early on, it might be best not to take him all the way.
Nidoran Male, on the other hand, is well off. In addition to learning the moderately useful Horn Attack and Double Kick early on, it can evolve two times in rapid sucession. You can easily end up with a late-game tier Pokemon just after or even before you beat Misty. That said, Nidoking is reliant upon TMs for most of its quality moves, including the likes of Earthquake.
Spearow and Fearow are arguably better off than the Pidgey Family. These fast and powerful mons mostly rely on Peck and Drill Peck, two moves shared with Doduo, but on their own rights, they use them pretty well. They can also use Fly, Mirror Move, and Agility. That said, their reliance on Flying attacks leaves them wanting in the variety department.
Zubat sucks Gen 1. It doesn't get a reliable attack until level 15, making it only slightly more useful until Magikarp. And unlike Magikarp, Zubat never becomes a Gyarados. Sure, Wing Attack is nice, and so is Confuse Ray, but you have to do so much work to get there, it's usually not worth it.