With Lanna Jin
The invisible man/woman: The ultimate laissez-faire approach. You have the freedom to choose the ideas and projects that interest you, and the responsibility to make them work. Freedom can be replaced by frustrations when you need a signature, some support, or a manuscript commented on.
El generalissimo: "Here's my idea, now go do it." These labs are usually run in a top-down manner. Day to day operations are fairly hands off though, giving you room to work through those problems on your own. El generalissimo will reward their supporters well for good work.
The coach: The coach provides you the best of both worlds: enough rope to explore your ideas, but not so much to hang yourself. They are available for troubleshooting and brainstorming, but you ultimately have responsibility for your project. But if you rely on them to much, it's going to be hard to function without them.
The micromanager: These supervisors expect regular presence, frequent meetings, records of progress, and milestones to be met promptly. If you like working from home, leaving early or starting late, or need lots of freedom to be most productive it could be a poor fit. For students who thrive on structure and prefer set goals though, this might be an ideal environment.
The superwoman/superman: This career superstar has made their name, possibly quite early, and they are passionate about their science. This can make for an exciting and successful lab experience, as new ideas and opportunities are always on the horizon. But since they have so many demands on their time, sometimes their capes (and they) are feeling a bit ragged.
The silverback: Labs of influential individuals can be an amazing opportunity for a graduate student. Silverback experiences might be quite variable, depending on how involved they are in day to day lab activities, their travel schedules, and the size of the lab. When they are available, they have a lot to teach a student about making a successful academic career.
Bad idea: This corner of the tradeoff (low interest in science, poor establishment in the career) probably doesn't exist in tenure-track faculty. If you do manage to find such a person, run away.
The unknown: A motivated but still unestablished supervisor is a blank slate. Their early career state means that they might have time and energy to devote to you and be especially motivated to see you and the lab succeed. On the other hand, they may not yet know how to manage people and their supervisor style could morph into anything - the coach, the micromanager, el generalissimo. A bit of a gamble.