What should I study to be a professional graphic designer and what about online classes?

First of all you must love design and everything relates to it. Regarding the software you should learn: Photoshop, Illustrator and InDesign are some of the tools you should first study, in order to visualize your designs and move forward. There are tons of online classes and courses, but to start I would recommend to check some great courses on Lynda.com.

The Graphic Design have a lot of branches for specialisation, the most important to know the essential, study how is effective  the graphic design. since our rise like a human being the pictorials paints in rupestrian  art,   until our more advanced computer graphics, this career is based on one important premise "Communicate across images and colours"Depending on the client, the graphic designer must have very clear the use of software based on pixels or vectors.Having said this you can use Youtube and subscribe to lot of specialised channels. All depends on what software´s choices.