You used good judgment with your fish store. DO NOT purchase coral for your goldfish tank! It will slowly dissolve and change the chemistry of your water, and anything living in it could be dangerous, even deadly, for your fish.
As for water changes, particularly with your stock, you should be doing large regular water changes. I would recommend a minimum of at least 50% once a week. Keep it at the same temp as your tank, and add a water conditioner such as Prime or API Stress Coat.
You also asked whether 1 filter was enough. I would be curious what kind of filter it is. If you have a simple HOB (Hang on Back) model, I would be doubtful. If you are using a sump or a canister filter, it is possible. Do you know what kind of filter it is?