The cheapest filter is probably a corner sponge filter like the one in the following link. There are lots of varieties of this type of filter and they can be blue, grey, yellow or white. The colour doesn't matter and is simply different brands. Some will have a lead weight in them to hold them down in the water. Others will need a small weight tied to them to keep them underwater. A small fishing sinker can be used to hold them down.
http://www.leemarpet.com/product/fi...37/lees-dual-action-triangle-foam-filter.html
Corner sponge filters run off an air pump like the ones in the following link. Air pumps come with 1, 2 or 4 outlets. The outlets are where the air is pumped out of the pump. You only need a 1 outlet air pump unless you want to run a filter and an air operated ornament. Sometimes the 2 outlet air pumps are a similar price to a 1 outlet pump, in which case buy the 2 outlet pump. but a 1 outlet pump should be adequate.
https://www.petbarn.com.au/fish/air-pumps-aeration-accessories
The air pump is plugged into a power point and pumps air into the aquarium through a piece of plastic tubing called airline. One end of the airline is plugged into the pump, and the other end goes onto the filter.
The air pump does make a bit of noise so get the shop to plug a few different pumps into a power point and turn them on to see which one makes the least noise. Put a piece of airline on the air pumps when listening to them.
----------------------
Another type of filter you could look at is a power filter. These have plastic cases that hold the filter sponges, and use a water pump to pump water through the filter media (sponges). Power filters pump more water through the filter materials and this helps clean the water up quicker. However, they do cost more.
There are 3 main types of power filter. The cheapest power filters are internal power filters. They sit inside the aquarium and have a small sponge in a case with a water pump (powerhead) on top of the plastic case. The water is pulled through the sponge and pumped around the aquarium. They only have a small sponge and usually create too much water movement for a small aquarium.
Another type of power filter is the Hang on Back (HOB) style. These are a plastic case that hangs on the side or back of the aquarium and sucks water into the filter by a water pump. The water flows through filter materials and then flows back into the tank. The best HOB filter is an Aquaclear. See link below. they come in a range of sizes and turn over a lot of water but it is returned in a calmer way so the fish don't get blown around as much.
https://www.filtersfast.com/P-AquaC...MI3rblhMLA2gIVkoK9Ch3OEgAMEAQYAiABEgKDCfD_BwE
The last type of power filter is an external canister filter. These are a plastic container/case with a pump on top. They are connected to the aquarium by plastic tubes. The aquarium water drains into the filter by via the tubes and is filtered by materials inside the plastic case. The water is then pumped back into the aquarium. These have a lot of filtration materials and work well but are the most expensive out of all the filters.
----------------------
My personal choice for a beginner would be the air pump and corner sponge filter, or an Aquaclear 30 HOB if you can afford it. It depends on prices and how much you can afford. There are other brands beside Aquaclear that are quite good too, so a cheaper brand might be available to you.
