Hi Nel and welcome to the forum
As a general rule it is better for the fish if you cycle the filters before adding fish. This means the fish are not subjected to harmful substances like ammonia and nitrite. However, if you are willing to test the water and do regular water changes, you can have fish in the tank while it cycles.
You get the aquarium and take it home. Don't have anything heavy in the tank while you are transporting it home. Put the aquarium on a blanket while it's in the car to help cushion the base. When you get the tank home rinse it out with tap water and then put it on a piece of polystyrene foam and have that on a hard flat level surface.
Go and buy a couple of new buckets and use a permanent marker to write "FISH ONLY" on the buckets. Use those buckets for the fish tank and nothing else.
Wash the gravel in a clean bucket of water. Take the bucket outside onto the lawn. Have a couple of inches of gravel in the bottom of a 10-20 litre bucket. Use a garden hose to squirt the gravel in the bucket. When the bucket is about half full of water, tip the water out and squirt more water in. Do this 4 or 5 times for each lot of gravel you clean. When the gravel is clean, put it in the aquarium.
After the gravel has been added to the tank, you can put some ornaments in and fill it about 3/4 full with tap water. Add a dechlorinating agent (water conditioner) to remove the chlorine/ chloramine from the tap water. Then set up the filter and heater. You can also add any live plants now and then top up the tank so it is an inch or two below the top and turn the light on.
You can contact your water supply company via telephone or website, to find out if they add chlorine or chloramine. Most water conditioners recommend using a double dose for chloramine.
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When you are talking to the water company, you can ask them what the GH (general hardness), KH (carbonate hardness) and pH of your water is. If they can't help you, take a glass full of tap water to the local pet shop and get them to test it for you. Write the results down (in numbers) when they do the tests. And ask them what the results are in (eg: ppm, dGH, or something else).
Depending on what the GH of your water is, will determine what fish you should keep.
Angelfish, most tetras, barbs, Bettas, gouramis, rasbora, Corydoras and small species of suckermouth catfish all occur in soft water (GH below 150ppm) and a pH below 7.0.
Livebearers (guppies, platies, swordtails, mollies), rainbowfish and goldfish occur in medium hard water with a GH around 200-250ppm and a pH above 7.0.
If you have very hard water (GH above 300ppm) then look at African Rift Lake cichlids, or use distilled or reverse osmosis water to reduce the GH and keep fishes from softer water.
Your tank is not really big enough for mollies and platies or guppies would be a better choice. Platies are generally healthier than guppies and have bright colours than female guppies, so might be a better choice for your child. Try to get all male or all female platies so there is less stress from males trying to breed with females.
Male platies, guppies, swordtails and mollies have a long straight anal (bottom) fin. Females have a fan or triangle shaped anal fin.
Having said this, find out what the pH, GH and KH are before choosing any fish.
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After the tank has been set up, let it run for at least a couple of days, preferably a week. Then get some fish. You should also buy a bottle of liquid filter bacteria supplement. It is beneficial filter bacteria in a bottle and you add it to the tank on a regular basis to help get the filter cycled quicker. I recommend adding a double dose every day for a week, then pour the remaining contents into the tank. Try to add the bacteria near the filter so it gets drawn into the filter where it belongs.
regarding the filter, there are several types available including air operated and power filters. Air operated filters require and air pump to pump air into the water and this causes bubbles to rise up thru a tube in the filter. Water gets drawn up with the bubbles. Air pumps can be noisy and a lot of people don't like them because of that. But they are cheaper than power filters and do work.
Power filters have an electric motor sealed in a plastic resin to protect the components and stop them going zap. They have a plastic case that contains filter media like sponges, and the water flows through the media and is pumped around the tank. They are generally quiet although they do produce a slight splashing noise if the outlet is above the water level in the tank. Power filters cost a bit more and usually produce a strong current in the tank, but most are good filters.
If you get a power filter, get one that does not contain filter pads or cartridges that need changing every month. Find a filter that has sponge, maybe ceramic beads and carbon. You don't need the carbon or ceramic beads and I prefer to just have sponges. But most companies put carbon and ceramic beads in their filters. You can normally buy extra sponges for most power filters.
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HAVING FISH IN THE TANK WHILE IT CYCLES.
If you want to do a fish in cycle, add 3 or 4 fish and feed them 2-3 times a week. Do a 75% water change and gravel clean the substrate 4-8 hours after feeding. You should also monitor the ammonia and nitrite levels and do a 75% water change any day you have an ammonia or nitrite reading above 0ppm.
Make sure any new water is free of chlorine/ chloramine before it's added to the tank.
After the filter has cycled (usually between 4-6 weeks), you can feed the fish each day and do a 75% water change and gravel clean once a week.
If you have some live plants in the tank, they will help keep the water cleaner and keep the ammonia levels lower so there is less stress on the fish. Floating plants are the best for removing ammonia and Water Sprite (Ceratopteris thalictroides/ cornuta) is a good plant to start with. It floats on the surface, grows rapidly and can be planted in the gravel.
When you add the bottled filter bacteria, add it after you do a water change.
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CLEANING THE FILTER
If you get a power filter or an air operated sponge filter do not clean it for the first 6-8 weeks, otherwise you can wash out the good filter bacteria and slow the cycling process. After that period, you can clean the filter once a month, or more often if it gets dirty quickly.
To clean a sponge or power filter, squeeze/ wash the filter materials/ media in a bucket of tank water and re-use the media. Tip the bucket of dirty water on the garden/ lawn.
Rinse the filter case and motor under tap water.
Wash the impellor assembly (magnet with 3 or 4 plastic blades on one end) under tap water. Be careful when removing impellors because some have a ceramic shaft that goes through the middle of them and this can break if you are rough with them. Most will also have a rubber grommet on each end of the impellor shaft and some have a plastic washer under the rubber grommet. Don't lose these parts. You can wipe them with a tissue or paper towel, or rinse them under tap water. If you rinse under tap water, put the items in a sieve and put that under the tap water so the parts don't get washed down the drain.
Reassemble the filter and get it running.
If you are confused about different filters, find out what is available at the pet shop and post their names and details on here and we can recommend a filter for the tank.
The shop should also be able to show you how to take the filter apart and put it back together.
