I can see a ship of Minbari Rangers being Earth's first contact. The Rangers were less isolationist and adding some Rangers to the crew might work.
I really like the idea of the Minbari sending Rangers to facilitate first contact with humanity, and has cemented for me the idea of having a Minbari as part of the Enterprise's crew compliment, with said Minbari being both a Ranger and an official ambassador.
How would the Vulcans respond to this, the Minbari gaining a new ally so close to their Homeworld? The Andorians, with their hostilities with the Vulcans? Would they try to court the Humans away from the Minbari, or try to establish better relations with the Minbari?
Do you want to run with the idea of the Andorians being the ones who ended Centauri dominance and the Narn allied with them?
Since I see the Vulcans being very preoccupied with their conflict with the Andorians, I didn't see Vulcan/Human first contact happening until after the Enterprise began her mission of exploration. I do think it would be interesting, though, for the Minbari to be basically using humanity's desire to explore the wider universe as a way to facilitate the establishment of a unified universe, which the Vorlons want to have in place should the Shadows ever come back, and the Vulcans - being the somewhat emotional beings that they were in the 22nd Century - reacting negatively to the idea of the Minbari and a ship full of humans 'interfering' in their affairs, especially with regards to the Andorians.
Regarding the Narn, I really see them being more akin to the Orions and the Ferengi, since I think it fits their reputation as arms dealers and a 'neutral' power who'll basically curry the favor of anyone so long as it can help them establish themselves as an interstellar power.
I see the Centauri being the kind of people who've pissed off a lot of other alien races because of their aggressive hunt for territory, so it might be interesting to explore the idea of conflict breaking out between them and the Andorians (since I like the idea of the Andorians being the universe's biggest and baddest warrior society), with the Narn - being the Centauri-haters that they are - forming an alliance of sorts with the Andorians in order to 'stir the pot', as it were.