Finches are great. But if you had them flying freely, you would need to be very careful. They can hurt themselves so easily. Flying into the blades of ceiling fans. Flying into mirrors or windows. Also, if you get males and females, you will have them nesting in some unexpected places.
If you have a spare room, you could get a very large cage. And I guess a chair for you. Leave the cage opened so they can come and go as they please. But keep the door closed. No mirrors. Keep the window covered. Make sure to have breeding nests inside the cage so they will use them.