I would like to get a birthstone but I don't know what mine is.
There is a lot of information on the internet about birthstones. You can choose between the stone(s) for the month you were born, or the stone(s) for your Zodiac sign. The following stones are the traditional stones by birth month as per the American Gem Society (http://www.americangemsociety.org/birthstones.htm)
April: Diamond (white topaz can be a more affordable alternative)
June: Pearl or Alexandrite
October: Tourmaline or Opal
November: Topaz or Citrine
December: Tanzanite, Zircon, or Turqouise