Personally I wouldn't even worry about making money right now. There is a lot to learn and when you start taking on clients you're going to be made aware of even more skills you didn't realise you needed. It's not the kind of thing you can attempt quickly and do well at. This is a career and will require some serious investment of your time.
I agree that you would be best off taking some kind of art course. You might not think it's relevant to logo design, for example, but it will help you to hone your creative abilities, which is definitely something required for logo design. From there you can look to take a graphic design course at college and then on to uni, if you so chose. However, you should be aware that you won't learn everything you need through traditional education. The best thing you can do is get into the habit of reading articles on graphic design which are plentiful and freely available online.
Another thing to consider is whether you want to become an art worker or a creative designer. Do you want to be the guy who takes orders from a non-designer and are paid for your abilities to use tools like Photoshop - or do you want to be the one in control of the entire project, building a brand from scratch and making all your own decisions. Also think about and research the differences between employment and freelancing. If you value creative freedom, freelancing might be a better fit for you but it's a much riskier path to take.