In terms of the difficulty of pinning down a definition, "desire" is quite like "pleasure." They're also quite alike in terms of pinning down a workable Epicurean ethics.
We've given a lot of effort to understanding what Epicurus meant by "pleasure;" the same effort needs to be applied to understanding what he meant by "desire." And that is not to imply in any way that they are the same thing: they're not. I tend to agree with how Julia and Todd are interpreting it, and I also agree that a good look at the original passages in the Greek may be helpful (by someone who understands Greek, not by me!)
As for choice: between desire and pleasure or pain lie choice or avoidance.
(Oops, I see that I missed the two posts above.)