For reasons that I cannot discuss, I may have to make a decision soon between playing the game in co-op first, or not playing it until later. I'm pretty much just interested in the way they handle the story, so will I be missing out if I play co-op instead of single player?

Nothing is different in co-op. Your spartan is shown in cut scenes. Nothing is handled different cept that you got a buddy with you. 

reasons you cannot discuss? You've been sworn to secrecy regarding the campaign of Halo: Reach? I'm curious now. :)

Here's a better question: Does the same Halo game need to be played after five times?

Halo in general is a very accessible shooter. Bungie have made sure there's no great prerequisites to just jumping in and playing.