You got an interview! It is so exciting! There are so many decisions to make. You need to prepare for as many as three talks, research, chalk talk, and sample teaching. You also need to carefully research the department and its members, as I have explained here. But then the dilemma rears up. They want you to come talk in a week, they say.
You are torn. After all, shouldn’t you be ready? Why not drop everything and get it over with in a week? Don’t do it. It is unreasonable to expect someone to come in a week. I’m not sure what I think an appropriate minimum time between invitation and interview is, but it is at least two weeks and maybe even a month.
Will asking for a delay of two weeks to a month hurt you? I would say not. The thing is, usually just one person is doing the inviting and scheduling. It might be the head of the search committee, however, so you want to be nice. The real issue is these committees are not professionals at hiring. They do it seldom and are inexperienced at the organizing side of things, no matter how exceptional they are in their field. They may change around what they offer you. Try to be accommodating, but only if it works for you.
You gain no points by showing up early and less prepared than you might be. But don’t waffle too much. This is your first interaction with potential future colleagues and you want to seem easy to get along with.
Some people think you should try to play the interview order. Some say early is best because they fall in love with their first and never get over it. Others say last is best because you are the new and shiny person. I bet there have been studies on this, but I have not seen them. In my experience order does not matter. Congratulations on your interview!