These three are only in the beginning of the game where you are still blowing up mako reactors with Barret. If you played other Final Fantasy games, you can guess what happens to them. You never get to play as them in the game.
[Personality]
Well, Jessie likes Cloud, she makes that slightly obvious when she always tries to talk to him, take care of him, or more specifically when she made a special fake ID for him. Biggs and Wedge look up to Cloud, but there's not all that much about them.
[The Truth]
Warning! This section explains nearly everything about Jessie, Biggs and Wedge. If you don't want to know, then don't read!
You actually think there's some hidden fact about these guys? The only thing would be that they die, which is expected because all Biggs, Wedges and anyone in their group dies in an FF game.