Some random thoughts for what I'd look for if I'd apply for a PhD position again. Some of these are questions you have to ask directly, some you can't ask directly without being rude, but you can check the lab's homepage to approximate answers.
1) What is the average time from start to graduation? This varies strongly by country, with some ridiculous years in the US. Outside the US I'd be wary if it's >4 years.
2) How often does the lab publish per year? If 10 people work in the lab and the lab publishes only one paper in a mid or low-tier journal per year I wouldn't join
3) What's the work/life balance? Does the PI expect you to work on weekends or other ridiculous times?
4) What's the funding situation like? Is there a chance they'll close the lab after 3 years? Is there a chance that your own PhD won't be funded, or that funding stops?
5) Is the PI/supervisor nice? Are the colleagues nice? What does your current supervisor/mentor say about the lab, if possible?
6) Can you take parenting time off? Does the supervisor/PI have kids of their own?
7) Is the lab's focus on applied bioinformatics or methods development? Many bioinformatics labs focus on one of those two, choose the one you like more.
8) How many other bioinformaticians work in the lab? I'd be VERY hesitant if it's just going to be you, you won't learn much and you'll have no chance to work on your own projects. Sometimes people only want someone cheap to analyse their data, all you'll get out of it is mid-level authorship, not enough to start a career
9) If you're into open source, does the lab publish open source? Same for open access.
10) Can you find a lab alumni and ask what they thought of it? (mileage may vary, sometimes you'll find someone who just didn't click personally, giving you a image that's worse than it actually was)
11) How many current/past lab members have side projects, run workshops, mentor etc.? Indicates a freedom to pursue own interests
12) Is there an industry component, or some other non-academic part?