Normally, graduate students at my university go through three rotations. I've done two and will need to choose a permanent advisor after this next one. So choosing a rotation is similar to choosing an advisor, yet the philosophy can be slightly different.
1) Funding: Does the PI have funding for at least one year? Having that planning time to find other sources of funding without having to TA is indispensable.
2) Choosing a permanent advisor: The purpose of a rotation is to find an advisor and lab I am comfortable working with, as this will lead to a happier and more productive few years of my life.
3) New skills: Doing rotations in multiple labs will give me perspective. I should be learning different skills from each rotation.
4) Research interests: I should find a lab with research interests that align to mine. I don't want to be stuck working in a field I don't enjoy for the next X years.
5) Prestige: An advisor with strong industry connections can leverage those connections to help me break into industry or finding funding for my startup. A recommendation from a professor famous in your field can be my ticket to a tenure-track position.
How should I reconcile these different points? I'm a bioinformatics grad, if that makes a difference.