Let me make this clear, there is no fixed specialization that will help you make it into counseling.
For working professionals: Companies that visit the campus for placements usually prefer Finance and Operations background. People with a technological background opt for tech consulting while many go for Sales and Operations consulting as well. The companies are not interested in specialization, rather they look for how good your CV is. So, we can say a guy from a pure manufacturing background who is currently studying marketing can also make it into consulting.
For freshers: The best specialization to choose to make it into a big consulting firm for a fresher is Finance. The concepts included in the Finance specialization are more connected with consulting. So if your area of interest covers both, Finance and Consulting, then opt for Finance while the target for consulting. As far as Operations is concerned, it’s not easy to get admission. Even if you do the chances are lower unless you do internships and projects.
Lastly, remember there is no direct relation between the choice of specialization and placements. Even if you fail to get into your desired company, know that it is not the end. You can slowly achieve your goal provided you are certain of it and are working hard towards achieving it.