"Graphics" is a pretty general term, so you might want to be more specific about what you will be working on. However, in general, you should learn a good imaging program like PhotoShop and a good layout program like PageMaker or Quark. After that, take on an illustration program like FreeHand or Illustrator. (I prefer PhotoShop/PageMaker/FreeHand, but others will advise differently - it just depends on how your brain works and therefore what is most comfortable for you.) Once you've gotten into these you will discover what else you need. For converting raster images to vector, there is a great little program by Adobe called Streamline. It comes in handy. As far as books go, one of the best I've found for understanding scanning and resolution is "Real World Scanning and Halftones" by David Blatner and Steve Roth (Peach Pit Press). If you want to get into the web, there are a lot of good books. You will want to get a good editing program like Dreamweaver eventually, which in theory lets you make pages without knowing HTML. I like Dreamweaver a lot - but you will need to learn HTML to keep from pulling your hair out when things don't go right. Another good HTML editor to learn with is HotDog out of Australia. If you get into web design, the best advise I can give is don't freak out when you see ALL there is to know (HTML, DHTML, XML, Perl & CGI scripts, ASP, JavaScript, Java, etc. etc. etc. - you'll never learn it all, so relax and just take it one step at a time. As you grow you will be able to decide which you need and want to learn and which you want to farm out.
Good luck.