Good questions! Regarding your first inquiry, it’s not an either/or: You can have a coach AND a mentor! While there are some similarities in these two types of relationships, they have different characteristics and serve different purposes.
A mentor is more of a trusted advisor, perhaps someone who IS where you’d like to be in the future -- for example, a current or former CIO. This is someone from whom you can learn the rules of the road and the tricks of the trade in your field and in your position. Someone who might take you under his or her wing, show you the ropes, share their personal experiences with you, and allow you to learn from their mistakes…and from their successes. They can help to open doors, be a reference, and a resource, and someone from whom you will benefit from the wisdom of their experience and the power of the relationship.
Now, as far as coaching: A coach is someone who is trained to perform this function. Almost anyone with experience can potentially serve as a mentor; not everyone can or should be a coach…or will be a GOOD coach, or the RIGHT coach, for you.
As for the coaching process, every coach has a different process, so it’s about finding someone who is a good fit, and with whom you feel comfortable and have chemistry, as well as respect, and trust.
Additionally, you seem to be talking about three separate, though related, things: a career coach; an IT-competencies coach; and a leadership or executive coach. It may not be impossible to find, but to me it would be a stretch to think you’d be able to get all three things from the same person – no matter how good a coach he or she is!
As I’m running out of space, I’ll stop here. But you are asking all the right questions, and I want to say that your proactivity, self-awareness, and insight in recognizing the benefits of seeking professional support to help you take your career to the next level are good indicators of your leadership potential. Good luck!