[Eomer of the Rohirrim]

I thought Legolas and Gimli were chosen because they were younger than other Elves and Dwarves and would therefore find it easier to get along with each other, not being caught up in the Elf/Dwarf feud and all.
Boromir wouldn't have gone all the way to Mount Doom. He was going back to Minas Tirith anyway and would accompany the others until the path divided.