Let me clear some of your questions
SAP is an ERP i.e. Enterprise Resource Planning which means SAP has developed software which caters to various Functional domains in the organization like Finance , HR , Sales , Materials Management , Quality Management , CRM etc .
SAP ERP has various Modules like SAP FI/CO , SAP HCM , SAP SD , SAP MM , SAP QM etc.
since you have core HR experience , you will fit in the SAP HR module , again in this you can be Functional or Technical Consultant
Functional Consultant - you will be responsible for Configuring the various sub modules of HR like OM (Organizational Management , PA (Personnel Admin) , Time Management , Payroll etc .. here there will be no coding .
Technical Consultant - these are the Programmers who work on the ABAP language on which SAP is developed , they are responsible for coding and Customizing custom Reports , Interfaces , Enhancements etc .
Regarding what Important things to learn , SAP is like an Ocean , so you should try to learn the module in which you have the core experience , in your case its SAP HR . Once you have learned and completed some Implementation Projects then you could look to expand your skill sets .
Hope this answers your questions .
Best of Luck !!!
25th February 2014 From United States, Woodcliff Lake