Comment by reedwhistle

For genomics, look into viruses, in particular RNA viruses like influenza and HIV. You can fit the entire genome on your screen and learn to read it like code! There are some good text books about viruses that include genomics from scratch (I can't find the one I used now but could look later if you're interested). My advice would be to learn the biology first and understand why we care about genomes before looking into the computational stuff.