Self-taught, and now I have been doing graphic design for more than 7 years:)
On the software side, you must learn photoshop to handle bitmaps and two others to handle vector images (Illustrator and coreldraw). You can choose one of them, and I suggest you learn Illustrator, because this software and photoshop are produced by the same company and have good compatibility. And coreldraw's file can't be opened in photoshop. .