There’s not a “correct” type and goldfish can be kept in tanks that use either an external or internal filter. However, an external filter is usually worth the extra cost if you can afford one. As they sit outside the tank, an external filter can contain more filtration media and can therefore do a better job of cleaning your water. External filters can also be hidden away in an to avoid interfering with the look of your aquarium and have the advantage of not taking up valuable space inside the tank.
Aquarium Filtration Information The Total Picture - Tetra-Fish
@Mars Firstly gold and koi fish are among the dirtiest of all fish through all types (cold, tropical, brackish, black, marine). They like most bottom feeders or "clean up" crews actually produce the most amount of waste. But this could of been caused by alot of other factors as well. Firstly how much are you feeding? Personally the 2 minute rule is b.s. You should feed very little 2-4 times per day. Remember fish don't have breakfast lunch and dinner, they are opportunistic and eat throughout the whole day. Secondly how much light are you allowing? Remember that if it's near windows sun light must be added into account for algae and bacterial blooms. Thirdly how long did you cycle? Most people believe fish can be added right away, even if they bought the so called "beneficial bacteria" water supplement. This is also untrue. You can't just add something expect a healthy colony like magic, it must cycle. Lastly the biggest downfall of most aquariums is the hobbyists. Lack of patience, over cleaning, introducing chemicals through various means. Just a few tips, always use hot water no soap to rinse up to elbows before sticking hands in. Ditch the carbon as when it absorbs all it can will leech it back into water and is essentially USELESS for aquariums other than for medication removal. Go with a sponge or foam pad in course medium fine layout. This will trap larger debris before reaching the fine floss that will hold much more benefical. Remember your filter holds the most beneficial bacteria in your tank and when you remove cartridges you remove your colony. Just rinse the sponges or foam in tank water you pull out during water changes to unclog. These only need changes every 1-3 years. Also never gravel vac entire tank do 1/2 of it every water change. And live plants can harm a tank if you don't have proper co2 exchange stay away from plants unless your read up and prepared to. Airstones don't do what people think, the bubbles do not add oxygen, the surface disturbance does. It releases co2 and allows oxygen to be basically ducked back in. Switch to gentle powerheads or an extra filter for the added surface distubance. But account for your lights, motors of all equipment, including bubbler pushing ambient air into your tank. Which in your case should be cold for fish meaning quite a bit lower than degrees. Most larger koi/goldfish tanks have chillers on them which even bring them down to just above freezing. The added heat could be stressful on your fish.
Aquarium filters scale up in size based on how big your fish tank is
For most tanks, one filter is plenty. If you stay on top of things you should have no trouble keeping your aquarium safe and healthy for your fish. Choosing the best aquarium filter is a big step in that process.
Tetra Aquarium Power Filters and Fish Tank Filters