10 gallon is really too small for Goldfish, they get big and very messy. The sheer amount of mess they make can overwhelm the very small 10 gallon volume. For more than one Goldfish you're better off with over 45-55 gallons. Goldfish should only be kept with other Goldfish of similar variety.
Instead go tropical, pop in a 50w/100w heater set to around the 75F mark, and have a read through this:
http://www.theaquariumwiki.com/10_Gallon