They need exercise to stay fit and healthy. Cramped caging can create many problems. Cage length and width are more important than the height of the cage because of the birds' natural flight pattern. Next, the pair will need a place to lay and incubate their eggs and hatch their babies. There are several types and sizes of Finch nests available.
Many people use the bamboo woven nests.
I use them because they are inexpensive and I can buy them at any pet store that sells birds. The bamboo nests come in two sizes, regular and large. Both work well but the larger ones are best for birds that tend to produce large clutches. Another popular nest is the wooden nest box. They can be mounted inside or outside of the cage.