The core jQuery library includes many effects of use to you: fadeIn, fadeOut, animate (can animate css style changes). You can change the z-index of elements to make them sit above other elements and use delay() or setTimeout to defer effects.
The jQuery UI library includes additional effects, but you probably need another library for controlling rotation. A quick search found
this one.I would have a look at the UI library to see if it has the rotation effect you need (I don't know if it does).
Although - I would suggest exploring the core fadeIn, fadeOut, etc., effects firstly, and decide about rotation at a later stage.