The great thing about bioinformatics is that there's so much data available online for free. Here are some links:

  http://www.ncbi.nlm.nih.gov/ - sequences, papers, and so much more
  http://www.expasy.org/
  http://smd.stanford.edu/ - microarray data
  http://archive.ics.uci.edu/ml/ - not biology related but good data sets to play with R

To navigate NCBI databases and learn file formats, you can read their documentation (http://www.ncbi.nlm.nih.gov/education/) or get any bioinformatics book.