When people ask me I generally give the perspective that the things you should consider when choosing the lab you will do your graduate studies include: 1. The advisor, and 2. The project.
The advisor- as in: What kind of an education will you get from this person? What is the advisor’s training record, do you work well with the advisor you are considering? How does the lab run? Are people who work in the lab excited about the work and about working for this person, and do their projects GO? Do people graduate from this lab in a reasonable time frame with a good body of work? Where have the people that have left this lab go on to? (With factors like $$ to fund the lab being equal and not considered in this analysis.)
The project- as in: If interest in the project is what drives you- are you going to love this project? Are you going to want to come in on Saturday morning to pull plates from the incubator to see what your Friday experiments yielded? What is your assessment of the risk of the project (this can be tricky for trainees to assess)… etc. My view of this is that some people are motivated by intellectual curiosity and they do best with problems that they are intellectually interested in.
Choosing grad labs based on advisor or project is not necessarily mutually exclusive though, there are all sorts of combinations of this.
Last night I heard a criterion for choosing a lab that I completely disagree with. Someone told me that they thought that the most important factor in choosing a lab was the methodology employed in that lab. HUH??? I had a hard time believing that I was hearing that and I even did that old trick where you try to buy yourself a little time to reply by repeating the question/statement. I guess I’m of the school that things that you want to get a great education and contribute to a field that interests you in grad school- not learn a particular methodology. I guess I’m of the school that think that you pick the problem, then you use whatever are the best tools to answer that problem. Period. That’s why I’m so against being wedded to a single or a handful of methodologies.