In the beginning of the manga, Luffy claimed that he wanted at least ten people to join his crew before entering the Grand Line (not counting himself).
Though most adventures in One Piece are random, there seems to be a ‘process’ for recruitment:
First, a situation arises where someone new is needed. The crew comes across someone who fulfills the criteria (i.e. Chopper the doctor, Nami the navigator, Franky the shipwright, Sanji the cook etc.). Luffy offers the person a position, and is usually turned down initially (which usually causes Luffy to comically “refuse this refusal”).
Meanwhile, a situation arises where, some way or another, Luffy ends up battling a ‘boss’ character, and the would-be crew mate battles an underling (i.e. Luffy vs Don Krieg after Sanji battles Gin and Pearl). The would-be crewmate typically defeats one of the villain’s henchmen, or otherwise plays a crucial role in the Straw Hats’ victory (for example, Brook defeats Tararan and reveals the zombies’ weakness, despite losing to Ryuma).
During the arc in which the new crewmate is introduced their backstory and dreams are revealed, (although Nami and Robin’s back stories were revealed later) thus convincing them to join the Straw Hat Crew.
Meanwhile, Luffy’s current crew would assist him in battling various enemies generally in rank of abilities and overall strength which is matched by whoever they are battling (i.e. Zoro vs Kaku, Sanji vs Jabra, Chopper vs Kumadori, Nami vs Kalifa), the enemies fought also have similar fighting styles (Zoro vs Hachi who are both swordsman, Sanji vs Kuroobi who are both melee fighting experts, and Usopp vs Chew who are both ranged weaponry experts), this is more consistent when it concerns Sanji and Zoro.
This process also led many fans to think Vivi would become a permanent crew member.
The only crew members not to follow this process were Jinbe and the female members, Nami and Robin, both of whom never helped fight an enemy during their joining and had their backstories fully revealed later on, despite initially being hinted at. Nami’s official recruitment was when Luffy, Zoro, Usopp and Sanji defeated Arlong and his pirates. Robin was the first to initially willingly join, and officially joined after Luffy’s crew came to her rescue from CP9. About Jinbe’s recruitment, Luffy invited him to join the Straw Hats, but Jinbe held it off until he had severed ties with Big Mom. He would later do so during the Whole Cake Island Arc and officially became a Straw Hat.
After the Straw Hats arrived on the Grand Line all the people that Luffy recruited have been abnormal people.