To be honest, without knowing whether this should sound conversational or formal, it is difficult to make an assessment. 'Everyone else' is grammatically and functionally acceptable and is more formal than 'the rest.' However, 'the rest' is not necessarily wrong: the rest simply means "the remainder"; those who are left over. I would consider referring to all other people as 'the remainder' to be less formal than stating that they were simply 'everyone else' (which is, essentially, the same thing, but perhaps a bit more positive).
I hope that was somewhat helpful. It is difficult to know what to say when these are without any context.