As you know if you read our Product Recommendation Post, my favorite brand of finch cage is Prevue Hendryx. I have them in black, white, large and small. For several pairs, or if you just want to provide lots of room for your finches, you'll want to invest in a "flight cage." Flight cages are just what the name implies, larger cages that allow for flight. Which, let's face it, isn't all that hard -- Gouldian finches are under 5 inches long! I've seen some sellers calling their cages "flight" when they are not, so let's take a look.
The right cage will be taller, although it might be just the same width as the single flight cage I usually recommend. So, something like 30X36X18.
I'm going to post a few cages I have experience with so you can pick somewhat knowledgeably. They're in no particular order. I have noticed that Amazon sellers are trending toward narrower cage widths -- 24 or 25" instead of the usual 30" width. please be careful and read the descriptions thoroughly. We do not recommend using cages narrower than 30" wide because Gouldians, like all finches need at least that much room to fly.