I started my own plant business many years ago. It is not easy and often requires significant cash outlay up front to get started. There are also many business considerations that are not plant related - insurance, taxes, environmental regulations, business registrations, incorporation, etc. All are important to the success of any business.
In any plant business, there is no substitute for hands-on experience. Academic courses can be very helpful, but learning-by-doing is essential.
I strongly recommend that you first find employment working for a plant retailer or landscaping company so you see and experience from the inside just what is involved. I think you will be surprised and possibly discouraged when you learn what is involved. By working for an existing company, you will not only learn but you will not have to lay out money in advance and can actually start earning money right away. Spring is a time when many plant businesses are looking for part and full-time help, so now is a good time to look for a green industry job.
I have a blog post on this site that is about the interior landscaping industry that may be of interest to you.