Let me share my view on this topic after being 3 years with McKinsey and achieving a promotion meanwhile... in a nutshell there's no one that will define your career whatsoever, and the Firm really proudes itself of the core idea of each person does each own McKinsey (sometimes it might even sound bulshitting for people outside, but it's the purest reality).
Now, let me discuss a bit more into detail your question:
First of all, there's no single answer fits all, as your autonomy to decide between projects varies significantly not only with tenure, but also with location (particular office) and even practice (if applicable). As a junior generalist consultant, it will be really difficult for you to chose your projects in most of the offices (US and London as some notable exceptions) - there are people to allocate you to the projects!. As you move upwards and gain experience and contact with Partners, the ones that liked you will try to push you for their projects, and you can proactively start moving yourself to get what you want (e.g., I really wanted to do a project in Australia, and I ended up being able to do it, even coming from an office where that doesn't happen often!).
On your second point, there's no such thing as a career counsellor. There are two figures: a DGL, who is simply the person in charge for presenting your case in the evaluation and promotion committees (in an unbiased way) and then you can have as many informal mentors as you want (i.e., persons to which you recur to discuss about your career and progression; not a formal role though).