Read and watch things that aren't action adventure or comics. You often find more characterization in one episode of Coronation Street than twenty episodes of X-Blobs from Mingo . As for classic fiction, it's as good a place to start as any. But the best drawn, best written comics are always those that stand the test of time - and keep a writer or artist in work in a very competitive market place. Self publish if you can afford it.
Good editors like to see published work, even published work in fanzines.
I started my career in comics by publishing my own fanzine. It never made any money and we only ever produced 200 copies every issue, but several people who started with work in it have gone on to work in comics, including myself. Dave Jones now works on Viz and Nick Miller has drawn for many comics. Dave Sim's Cerberus be the archetypal example, Eddie Campbell and Alan Moore's From Hell , Bryan Talbot's Luther Arkwright or Paul Grist's Kane . There are others, such as the delightful Strangehaven , but they are sadly still few and far between.