Finches are wonderful little birds. At the place I used to work we did pet rescue and we had many finches. We had mostly zebra finches, a few society finches, and a few goulden finches. We also had two Java Rice finches, those were my favorite.

Like Cathy said you'll need a flight cage. The one she linked to is a good size, however the bars are too far apart. This is a good cage and very simular to the one we used for the colony of Zebra finches we had. Finches like to fly up and be high, so having a tall cage is important.