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.
Blue Lab Coats 
In a sense, the person is right. You want to join a lab where there are multiple methodologies being employed, and where you will have a chance to learn more than one of them. The most successful labs are those that deploy multiple methodologies, and even bootstrap new ones, to answer the questions they are interested in, not the ones that have a single big fucking hammer, and run around looking for fucking nails.
I’m somewhat leery on selecting too much based on the project. I’ve seen students take an advisor they feel indifferent about for a project they love- only to have the project completely fail or lose funding and have to switch work 2 years down the road. Then they’re stuck with an advisor they wouldn’t otherwise want.
I agree with CE. Additionally, maybe it was because I had limited research experience as an undergrad, but coming into grad school, I knew the general area of research I was interested in, but I had a hard time distinguishing what potential project sounded most appealing. I think this is amplified by the fact that potential projects are sometimes very vague and undefined at the point of time that advisors are interviewing potential students.
My advice has always been to choose based on advisor and lab atmosphere first. If the advisor is good, s/he will help you structure a project that you love.
I agree with CE and Liz. You certainly should be working on something that interests you. A corollary to what drdrA says is choosing a project that you’re so invested in that you can see yourself still working on it, even when everything is going wrong. But projects have a way of taking different paths… or sometimes dying altogether. So when selecting labs, I have placed a premium on the adviser and the lab atmosphere.
The methodology question can go a few ways. As PhysioProf points out, you can choose a lab where many different techniques are employed, and you have the chance to learn them. This approach allows you to do more “curiosity-driven” research, as you are not dependent on any one method. This is the route I have chosen. On the other hand, if you choose a lab using a single cool technique (not uncommon in some fields, like analytical chem), you may well be a commodity because of your expertise, but you will also likely be limited in the places you can work since cool techniques often require expensive equipment. You’ll also probably end up working on many different projects, so it may be a good path for those with project ADD.
CE, Liz, Biochem belle- I don’t think I meant to say that one approach is better than the other, or that they are necessarily mutually exclusive. Personally, I am one of those people who is motivated by the project, but that doesn’t mean that I would choose the most interesting intellectually stimulating project KNOWING the PI was a complete ass. I think it also depends quite a bit on the maturity of the student to KNOW what is a good project and what isn’t- and that can vary quite a lot- as Liz rightly points out.
I can think of someone who chose a lab based on both the questions AND the methodology. They wanted to use a mathematical modelling / theoretical approach knowing how much they hated and were bad at benchwork.
So they went to a lab that encouraged that approach to the questions being asked and a supervisor that could assist.
If you know that you want to approach a question in a particular way, then you need to find a lab that’ll allow you to do that.
Interesting post. I often see people joining labs, because they like the social atmosphere…ie: fun group that goes out a bunch. I don’t really think this is a good reason. I have seen people join said groups and then flounder because they don’t give a shit about the research questions.