Generally, I would figure out the size of the control panel and lay the components out before working on the art. That way, you can design around the components you're going to use. That way, you won't have say.... a character's head replaced by a button, or your joystick coming out of someones crotch.
As far as software, I would recommend using a vector based program so you don't have to worry about resolution right off the bat. However, if you don't feel comfortable using vectors to create your art, make sure you're working with at least 300dpi. Another good advantage to using vector based software is that you can also move your components around and try different configurations with minimal hassle.