Choose a subject area that inspires you. Genuine fascination with the area of research helps you to learn quickly and provides motivation to carry you through the times when experiments are not working out as planned.
Choose a laboratory in which the resources and facilities required for your project are available. It is also an advantage to have access to facilities and expertise that you only find out will be useful during the course of the project. Is the institute as a whole well resourced and does the staff work collaboratively?
Choose a laboratory with a strong track record of producing high quality publications. The overwhelming majority of students complete their studies with a PhD. Subsequent application for postdoctoral positions and fellowships is significantly dependent on the quality of research that has been published in scientific journals as a result of your PhD.
Large or small research group? In general larger groups publish more papers, but bear in mid that smaller groups are often more productive per person.
How have the careers of former lab members developed? This is not relevant for a very new lab, but for established labs this information can often be found on lab web sites or with a little detective work.
Management style. This varies greatly from lab to lab. Do want the freedom to follow up on your own leads, or would you prefer to have a very well defined project? Best assessed through interaction with lab members.