Hello! Jen and Michael already provided sound advice; but would like to add some info based on my 51 year long fish keeping experience. Fish and frogs eat each other in nature; mix them in a tank and it becomes an experiment until one does the other. From your fish choice proposals (Discus, Angels, Neon Tetras) it tells me they are based on looks and not of knowledge of the species and it's requirements. Good that you ask here because none of those would work. My recommendation is not to keep fish with frogs.

If using as feeders: set-up a Molly breading tank; quarantine parents and do anti-parasite treatments on them; feed them spirulina based foods; and then feed the grown babies to frogs. Before they are eaten you will have "fish in your tank."

Ammonia/Nitrite reducing bacteria populate surfaces. So you will have them mostly in substrate, the filter's pads and bio-media. You can rinse out the pads in tank water and re-use them in new filter if they fit. Or you can rinse bio-media same way and move that into new filter with new pad. This will leave pad in previous filter with new bio-media. Until you have new substrate seeded (2-4 weeks depending if you add bacteria to tank or not); do not replace any filter pads or bio-media. Just rinse in tank water and re-use. As Jen explained, that bio-media bacteria culture has adjusted itself to your goldfish needs. It will take time for it to adjust to your frogs. Adding them in stages is the smart thing to do. If you add all frogs at same time the filter will need more time to adjust and most probable your frogs will get an Ammonia spike followed by a long term Nitrite bath... not healthy at all .

In terms of bacteria loss, you can expect negligible loses during media cleaning and transfer unless you let it dry out. If tank's pH vary more than 0.2 units you could have more severe bacteria loses and even crash the bio-filter if there are major differences. Also, would recommend new tank matches old tank temp during filter set-up and then set up/turn on any heaters in new tank if required.

Finally, how long is your fancy goldfish (mouth to end of tailbone - do not include tail fin)? Reason I'm asking is because if it has not severely outgrown the 14 gal.; he is better being left in there. Last thing you want at the moment is that "Murphy's Law Strikes" and the loved by your family goldfish gets sick or dies. Trust me, that would create a problem for you and the frogs! Good luck !