After Gandalf's departure in The Fellowship of the Ring, it is undoubtedly Aragorn who becomes the leader of the quest. He takes charge of the Fellowship, holding them together and directing their next steps. The other characters defer to Aragorn's leadership.
It could be argued that Frodo is actually the leader. After all, he is the Ring-bearer, and both Gandalf and Aragorn defer decisions to him at times. However, Frodo typically takes a more passive role, as he lacks the knowledge and leadership qualities of Gandalf and Aragorn.
When considering who would be the best leader, it is important to consider what qualities you value in a leader. Should a leader simply be an excellent fighter? If so, perhaps Legolas would be the best choice. Should a leader simply be kind? If that's the case, then Samwise would probably be the best choice. However, a leader needs many qualities, including power, kindness, wisdom, and decisiveness. After examining the characters, ask yourself which one most contains the qualities of a good leader. This will help you come to your own conclusions about who was most fit to lead the Fellowship after Gandalf.