Yes you still need a test kit. You can buy a marine test kit that tests for ammonia, nitrites, nitrates and pH at most petsmarts for about $50 but its cheaper than buying them separately and you'll eventually need all four tests anyway.
You can get RO water at any Walmart, Jewel or Kroger at the water refill station. A lot cheaper than buying it at a fish store.
For a twenty gallon tank, a " hang on the back " filter rated for a 30g tank will work fine.