You can still use your rear derailleur but you will need a 9-speed shifter and chain. Any 9-speed STI will work but since you are upgrading, why not go all the way to 10-speed?

Are your current brakes single or double pivot? If single pivot, any of the newer Shimano double pivot brakes will work well but not the newest (5700, 6800) since they use a somewhat different cable pull. Look for 105 BR-5600 or Ultegra BR-6600 as a suitable set.