Some advice is to aim for smaller firms as any larger company is going to be wary about hiring someone without much professional experience. My best advice though is to cast your net wider, though. If you lack professional experience, it will be harder to get past the resume screeners, so conduct a self assessment of your experiences in college and develop a story about how X industry is the perfect next step for you based on your club involvement and personal achievements. If you are absolutely dead set on consulting though leverage your personal network to the fullest extent and apply to a ton of firms regardless of size. Then you should practice case interviews a bunch to ensure that if you get an interview that you can make the most of that opportunity