Generally feeding once a day, as much as they'll eat in a few minutes is plenty.
How much water do you usually change on a weekly basis? Goldies are very messy fish and I would expect that the nitrates hang out relatively high in their tanks.
I dont think goldfish do very well with plants, many times they'll eat or uproot them, plus I believe the plants like warmer water than the goldies (I could be wrong on that, I'm sure someone will correct me if I am)
Best (only) way to lower nitrates in an unplanted tank is to do water changes. Couple things though before you go crazy doing water changes. Test your tap water to see if IT has any nitrates in it. Then you know your tank wont ever be below that level unless you add a lot of plants. Also, test strips like the ones you got really aren't that accurate. They tell you "high medium low" etc and not a number on a scale. SO if you get bored/have the money etc you might look into checking out the other kind of test kits that have a test tube and bottles of reagents to turn your water colors. This way you can tell us what the number is...because depending on the tank and the kit...you may only have 40ppm and thats not TOO bad.