I was just wondering how everyone decided which mentor to work under. I've heard different advice; from pick a mentor with a lot of contacts to just pick one that you love the project you will be working on. Like would it be better for me to work in a big lab that is cracking out papers all the time or a small lab with more attention from the PI? Does it even matter? What did yall consider when picking the lab you now work in? Also, how important is this to the rest of your career?
Try to find a mentor you can work with personally. Talk to other students in the lab to try and get an idea of the mentor's style. Upper-year students are best, as your relationship with your mentor will change over time as you accumulate more know-how and become more independent. Note that a rotation does not really allow you to know all the mentor's foibles; they are usually on their best behavior with rotation students! Also, be sure to read between the lines when you talk to people. Few people will say, "I hate my mentor and we argue all the time!" They will just be more reserved in their recommendation, saying something like, "Well, he's very smart and can give good advice, but sometimes there are personal conflicts in the lab." Students who really like and respect their mentors will give unmitigated praise.
Re big lab vs. small lab, that is a personal choice. In general I would suggest that a small lab is better for a student and a big lab is better for a postdoc, but it really depends on your personal style and how independent you like to be. I would say that in a small lab you are somewhat more likely to get a good project (superlabs tend to give the important or central projects to postdocs and stick students with somewhat riskier offshoots), and you will certainly get more personal attention and direction. In a big lab you will get the benefit of a mentor who is experienced and successful and knows the ropes, as well as diverse input from a lot of talented postdocs with different backgrounds. You will also probably have more independence, which becomes more appealing as you progress and 'guidance' starts to seem more like 'interference.'
Regarding importance, you should treat it as very important. It's your PhD; make it a good one. The actual importance is hard to gauge because there are a lot of 'soft,' unmeasurable contributions. Your experience in your PhD may set the tone for what area of research you end up in (or whether you choose to stay in research at all).
In general, as for everything, the better your work in your PhD, the better equipped you will be to choose your path at the next step. If there is any chance that you will ditch the clinic altogether and go straight to postdoc, then it is extremely important that you publish well, as you will be judged on your PhD work by prospective labs. If you are certain to do a residency at least, then the importance is somewhat less. Any publications are generally a perk for residency applications, and I doubt a lot of PDs know the difference between Molecular Cell and Molecular Therapy. But better is always better, of course.