Strategy vs Management Consulting

I have a slight feeling that these questions might be stupid or obvious but I've struggled to find an answer. Regardless, feel free to throw shit lol.

I have a few questions about the differences between the two as someone who will be going to University soon. Although I know strategy consulting is a subset of management consulting, from what I gather strategy consulting is far harder to break into e.g. getting into strategy& vs just pwc, or monitor Deloitte vs just deloitte, so I want to prepare for the worst.

1) what's the difference in exit opportunities. At a management consulting firm is PE, VC or F500 still possible, or will I be stuck in management consulting for ever? Currently I'm thinking about going into corporate strategy afterwards but I don't want to rule anything out
2) what is the difference in salary in the long term. I'd want to earn at least 70'000 pounds a year at some point in my life, hopefully higher. Could I still get there without much more difficulty from management consulting? I know this is contingent upon the path you go down but I'm asking in general terms as I haven't decided on what to do in the long term.
3) as a management consultant will I still travel? This was a part of the job that would greatly appeal to me but isn't a deal breaker by any means.

I'm still relatively new to the industry so I may have made a few errors here and there. Anyways, thanks for any help!