Well, of the regular cast, they were the only ones who reasonably Could have gone.
Susan is only about 16 at the time.
Garibaldi was a Gropo.
Sheridan is the son of a career diplomat. But, he's not so senior they'd Miss him if he didn't come back.
G'Kar is a reasonable go between. He speaks the language. And, he's an opportunist. He expects to make a Nice Profit on the deal, one way or another.
It's dangerous. They are Pissed at Franklin. If he doesn't come back, they don't mind. But, Franklin did have prior Contact, having tried to save the Life of an injured Minbari. I'm sure there was a bit of hope that the Minbari would feel some small obligation to him. After all, Earthgov was Desperate, they were grasping at straws.
Yes, I like cats too.
Shall we exchange Recipes?
You have the only ambassador who has shown a willingness to help, even if it was for profit, and an experienced officer with connections. Since gropos who see Minbari don't live long Franklin going as an officer who knows what Minbari are like(somewhat) in person is not that unreasonable.
Is it a stretch? Perhaps but not that much of a stretch.
"The pink ones keep ya from screamin'." Grandpa
G'Kar went because the message to the Humans from the Minbari went through him.
Franklin can say whether they are Minbari.
Sheridan just won a major battle against the Minbari.
"Gideon says we all have things to hide."
"Does he? How unfortunate, I was hoping he'd come further than that. Well not that it isn't true of course, it's just that one simply doesn't have to say it."
Actually, I think Santiago selected Sheridan in spite of the destruction of the Black Star, rather than because of it. He knew that the move would tick the Minbari off something awful because of Sheridan's war record. But Santiago knew that Sheridan had an outstanding record on First Contact protocol (as General Lefcourt mentions) and had handled himself well in diplomatic situations with the League worlds both before and after the E-M war.
Sheridan's war hero status (and higher rank) may have made him more popular with certain folks back on Earth, but I don't think that would have been the reason enough for Santiago. The President believed in the Babylon Project and in maintaining good relations with the alien governments - especially the Minbari. So he wouldn't have lightly chosen someone like to antagonize them, and if he did he'd be certain that the person had other qualities that could offset the Minbari resentment. (Heck, if all he'd wanted was a gung-ho type he could have selected Gen. Ben-Zayn.
I suspect the after-action reports on the failed peace initiative (especially G'Kar's and Franklin's) played at least as big a role in Santiago's choice as Sheridan's nuking of a Minbair cuiser.
Sheridan: Are you trying to cheer me up?
Ivanova: No sir, wouldn't dream of it.
Sheridan: Good, I hate being cheered up. It's depressing.
Ivanova: So in that case we're all going to die horrible, painful, lingering deaths.
Sheridan: Thank you, I feel so much better now.
I'm gonna go out on a limb here, but I think you're all wrong.
It was, in fact, Clark who selected Sheridan. Santiago was killed, then Clark was sworn in, then Sinclair left B5, then Sheridan took command. It was my understanding that Clark chose Sheridan because he was disliked by the Minbari, thus keeping in line with his isolationist policy. The first time Bester encounters Sheridan, he says he was told Sheridan would be more cooperative. He figured they were on the same side, since Psi-Corps and Clark were scratching each other's back.
Clark hoped that the B5 project would fail so that he could say, "See, those damn aliens can't coexist peacefully, we need to get rid of them." He also, perhaps, hoped to have Sheridan as a loyal public figure, an example to the people. He deliberately arranged it to be a contentious situation on B5.
This was, of course, his greatest mistake.
"You do not make history. You can only hope to survive it."
Sheridan was first on Santiago's list as possible replacements for Sinclair. He put him there because he knew that Clarke would like what Sheridan appeared to be on his record while Santiago knew what Sheridan was really like. Santiago was suspicious of Clarke and this was one of the safeguards he put in place in case Clarke moved against him. If that happened Santiago knew Sinclair would be replaced.
"The pink ones keep ya from screamin'." Grandpa
It is a bit of a coincidence that Sheridan, Franklin and G'kar were on the mission together, but they needed to be regular characters, otherwise it would not have worked. Also, for reason stated by others above, in terms of the plot it is not too far fetched that they would be the ones chosen for the mission.
On another note, Sheridan was probably the first on the original list for the post as captain of B5. Sinclair only got the job due to intervention on behalf of the Minbari who wouldn't want 'Starkiller' to hold such a position (see 'Eyes' and 'Points of Departure'). When Sinclair was reassigned they would have picked the person at the top of the list which was in all likely hood drawn up by santiago.
Clark, for obvious reasons, would not have allowed the Minbari any say in the matter this time and, as stated in the show, he approved Sheridan due to his record. I can't remember the episode reference, or even the exact quote, but some one back on Earth tells Sheridan that he was given his possition because his record made him look like a "jar-head" who would simply follow orders. Exactly the sort of person Clark would want in such a possition, espicially given Babylon 5's potential threat to him as revealed in later episodes.
"Watch the Shadows, they move when you're not looking..."
Indications are that Sheridan was not on the original list (which mostly contained Admirals and Generals, given the high-profile nature of the assignment.) Sheridan would have been too provocative to the Minbari and might have caused them to withdraw from the project.
He was Santiago's choice to replace Sinclair, however, once the station was up and running, and the Minbari already on-board. Santiago must have figured that the Minbari were less likely to abandon the Babylon Project once it had been around for awhile and established some kind of "track record."
Sinclair was not a popular choice back on Earth, whatever the Minbari may have thought of him, and Santiago probably designated a replacement for him less out of concern that Sinclair might be killed or incapcitated than out of fear that he would be forced out for political reasons. (Which he seemed to be on the verge of for the entire first season.) Sheridan was a choice the "Earth-Firsters" would find palatable based on his record, while Santiago believed he would do the job the way Santiago wanted it done. Granted, this would piss the Minbari off, but hey, it's an imperfect universe.
The dialogue specifically states that Sheridan was "the late President's first choice to succeed Sinclair", so it is clear that he was Santiago's choice, not Clark's. General Hague later tells Sheridan that Clark went along with the idea because Sheridan - on paper - looked like an ordinary jar-head who would do what he was told.
All of this suggests that Santiago knew a great deal more about Sheridan than Clark, to whom Sheridan seems to have been little more than a name on a file or in a headline. I wonder if Santiago actually knew Sheridan, or at least knew people who did. Hague and Lefcourt obviously did, and regarded Sheridan as something of a protege. And Sheridan's father was well-connected in EarthDome. This may have gone a long way towards getting Sheridan the command.
Sheridan tells Ivanova that he was Santiago's choice to replace Sinclair in his very first episode, Points of Departure. (Ep. 201) He guesses that his experience dealing with the League Worlds and other aliens as commander of the Agamemnon was the reason.
General Hague goes into more detail about Santiago's selection of Sheridan and the reasons behind it in All Alone in the Night (Ep 211)