brutalvirginia, i do not recommend you attend training on your own. not a lot of people get successful with this strategy because training does not guarantee you a job. it is safer to join a company that will train you so you also get the needed hands-on.
penelope, what does an SAP support analyst do? since you have no SAP background, i assume you will do first-line SAP support. in our organization, first-line support mostly just accepts calls and solves the really easy questions. 2nd line support will deal with the less simple ones and 3rd line for the complex ones.
if you want to do advanced reading, you may do as xtine has suggested but more than that, i would recommend you really go through the company's business processes, SAP business blueprint and study their config for you to be effective at your job as support analyst. then later on you can explore all the other functionality of SAP so you can make improvements to the company's process/config.