Strategy consulting is usually the "elite" element of the consulting industry and most often referred to as Management Consulting. There is IT consulting (very technical and competitive - outsourced mostly), Financial consulting (Big 4 play here), Business consulting (I feel Accenture fits here best) and Management/Strategy consulting (MBB's are here). Strategy consulting used to be a separate elitist thing but it was combined/merged with Management consulting in the 2000's during the crisis. There are lots of resources on Management consulting and what it entails. Usually MBB's will attract customers with their case studies, roaster of resumes and talent on staff. They only hire best of the best from top BSchools for their management/associate positions but they also have plenty of Analyst roles for undergrads but also from elite schools with strong analytical skills and high test scores.
There are 2 main paths to get there:
1. On Campus recruiting - this is the best path. This may be along the lines of a career fair or 1-on-1 interviews at a special on-campus recruiting event or it may be through a full time rep present at the school who you have access to in the top 10. In this case you are competing with your classmates and other top 10 students technically, though I feel most consulting companies have a certain number of posts they look to fill at each school, so mostly you compete with your classmates in terms of your resume (getting selected for an interview) and then your fit/style/abilities. You have to sell yourself/present yourself favorably and they basically look how you would perform in front of a client, customer, and whether you have the energy, speaking skills, and a team player.
2. Applying through online job sites/company websites not through a defined school path. This is a harder path but not impossible. These firms are always looking at capable candidates. High GMAT Score is helpful to get their attention if you are attending a lesser ranked program.
There is more on the topic here:
https://gmatclub.com/forum/management-c ... 62916.html