The way the novels after Ender's Game work is that Ender is older (60ish years)and much time has passed. This causes the later novels in the series to be fundamentally different from Ender's Game. They are still worth the read if you like a slower more science/political focus read. I believe the correct order is Speaker for the Dead, Xenocide, and Children of the Mind though its been a while. If you don't you might try the Shadow series which follows Bean and what happens on Earth after Ender's Game. Shadow series is more similar in feel to Ender's Game then the rest of the Ender series. I haven't read the short stories and they are not required to understand the series at all.
Basically what Cal said.