The Minbari had fought the Shadows in the last war, and the Vorlons accompanied Valen
In the first Shadow War (1000 years prior to the show), the Minbari were the primary force fighting the Shadows. When Valen first met the Minbari (the events of which we see in the episode War Without End, Part II), he was accompanied by two Vorlons, who appear as angelic beings (you can see their encounter suits beside Valen).
The Vorlons' primary goal is to oppose the Shadows. The fact that the Minbari did so during the previous war, and their greatest leader was accompanied by Vorlons*, meant that they continued to be allies. We see that Delenn is one of the first to advocate for defeating the Shadows and is working with Kosh to do so.
Additionally, the Minbari very much support a rigid caste system and society. The Vorlons believe that Order is the right way to guide society (rather than Chaos as the Shadows believe), so a society that continues a strong tradition of Order is someone who will likely trust the Vorlons in their plans.
* It seems that the Minbari are one of the only races where at least some people know what a Vorlon really looks like, given that Dukhat and later Delenn had seen a Vorlon.