this might be a pretty late comment to your post, but I have had finches before - about 6 of them. they are nesting birds and do lay eggs if u provide them with a little house (something small, round with a hole in the front) and nesting material. they also love to bathe and hate to drink from their bathing water. Also they are active birds and like room to flit around in. Calcium is good for them.
I raise zebra finches in an outdoor aviary. They are colorful, fairly quiet (nice soft twitter) and need plenty of space to FLY. They will bathe every day if water is available. They prefer to drink from running water (I have a small stream for mine). They eat millet/canary seed mix and whatever bugs they catch in the cage. They love to forage in freshly turned dirt at the bottom of the aviary. They will also eat almost anything green & growing. I tried several times to plant part of the aviary with different types of sod but they eat it within a week every time. They need to have a nest box to sleep in even if you don't want babies. You can remove the eggs once or twice a week to keep them from hatching. I give mine a bunch or two of parsley every so often. I also throw the weeds from the garden in and they just love it. I give them the grass clippings from mowing my lawn to build their nests with. I will also give them burlap strands if I run out of grass in the winter. (plain uncolored burlap from walmart cut in 2 inch squares and pulled apart into the strands). If you spend enough time with them, they can learn to sit on your finger and eat out of the palm of your hand. They don't tame quite like the hookbills do(parakeets/cockatiels), but they are quieter.