Goldfish get too large for a 10g. You could have a betta. It could live without a heater as long as the temp doesn't go below 70F. A filter is good because without it you'd have to do frequent 100% water changes. You don't need an air pump. The filter should aerate the surface enough. Bettas don't like alot of current anyways.
Another option is guppies...but you'd need a heater.
One goldfish needs a 30g tank IMO
. Most of them get pretty big.