First, can you let us know your water parameters of the source water, which is tap (or well)? The GH (general hardness) is especially important, but while you're at it, find out the KH (carbonate hardness or Alkalinity) and pH. You should be able to find this data on the web site of your municipal water authority (if on municipal water, not private well). This is important, as some fish have preferences for soft water or harder water, and some manage in the middle.
Given the limited tank space, 10 gallons, your options will be limited. Tiger Barbs is not possible, as these require a group of 10-12 (they can be especially aggressive to each other in smaller groups) and this requires a 30 gallon or larger tank.
Goldfish is maybe possible, just one, provided it is one of the smaller sized variants. But I am not that up on goldfish, and if other members with more experience say no, I won't disagree.
Guppies can work. Males only. With females and males you will have hundreds of fry which may sound nice, but quickly becomes a real problem getting rid of them. Females can be impregnated even before the males get their colours.
When we know the water parameters it will be easy to offer other suggestions. Many of the smaller fish that suit small tanks will be wild caught and thus more attention must be paid to parameters.
Byron.