I worked for my Diploma thesis with zebra finches (anatomy of song control nuclei in the brain). About the real costs I cannot tell you. But I have some tips that could give you a hint of what you will need.
These birds are good breeders. They breed during the whole year. So you can easily generate your own colony and after several generations you have huge amounts of animals. They just need some cotton fibers to build a nest. Depending on your cultivation circumstances (large cage with many animals or small cages with one couple or single animals) you have more or less work (changing food, water and the sand). The sand needs to be changed one - 2 times per week. Food needs to be changed two times per day because they only eat the grains on the top. A lso you can give them cooked eggs.
Diseases are not a problem with these animals if kept in good conditions.
Therefore in my opinion they are not very expensive and very easy to handle.
Canarys are more problematic (they breed only one time per year).
In Europe (and I assume America) Zebra finches are cheap to buy, easy to keep and breed, and are cheerful undemanding creatures. They do not fight (much) unlike many species of small pet birds. They do very well in cages or small aviaries. You could have a big colony quite easily but if you only have two or three years you may need to be doing research rather than breeding finches. Housing would be cheap to provide and they are happy to be hot.
Seed alone is a calcium, methionine and lysine deficient diet. Unproductive Zebra finches can manage on seed alone BUT your stock will be bigger and healthier (as Stefan says) if you give them a source of calcium, which could be the eggshells crushed and protein from the eggs (hardboiled). However, indoor birds will need some vitamin D and I would suggest whatever you feed, the birds need a good quality powdered vitamin and mineral supplement on their seed each day as well as some small sized grit (suitable for canaries is OK). Initially they were desert birds but they do need access to water.
I only say all this because I have spent 40 years trying to rectify chronic ill health in badly fed captive birds