Mining is a good money making skill for a free player. Mining Tin or Copper can net you 20-40K per hour, which is great for a beginner. The price of Tin and Copper may change over time and they are not always the same price. Simply mine the most expensive one.
With only 1 mining to begin this task, Copper and Tin are a great place to start. You should use the best pickax you can to mine, and buy newer pickaxes when you can use them.
Copper and Tin can be found in Al Kharid, Southeast of Varrock and in the beginner mines around Lumbridge. I recommend the Southeast of Varrock spot because it is pretty close to a bank and there are a lot of Copper and Tin rocks.
After mining and banking all the ores you have, sell them on the Grand Exchange for profit or save them for smelting.