Here is what I am doing @Account Closed. I graduated college with similar aspirations which I still have but I wish someone would have given me the advice I am about to give you. (Not saying this is the greatest advice ever but it would have helped me tremendously).
Start whatever business you want to start NOW(that doesn't mean selling, it means learning and setting up the systems, infurstructure, etc.). Don't wait till you graduate, cause then you'll have loans and you'll have to get a job which will get in the way. My advice is learn how to wholesale, make and save money during college. Use said savings to flip or buy rentals while you're in college. Trust me, you have enough time. If you want it, you'll skip those parties/chill sessions with your college buds. Start making relationships with hard money lenders, flippers, investors in your area now! If you don't want to be working once you graduate, you have to start setting yourself up now and even start making those investing moves now!
On whether to start investing or start a business first; I'd say start investing in cash flowing assets. flip a couple house, get out of any and all debt, don't go buy a new car after college like your friends, save that ****! Once you're debt free and you're expenses are low, you're living for free in one of your apartments, you'll have the freedom to start that business and not worry about taking money from a start up, growing business.
Many new businesses fail because the owners are taking money out for themselves instead of reinvesting. That's cause they didn't think about making sure they were secure which will allow them to concentrate on efficiency and growth!
Happy learning!
Good luck!