Each filter, however it is constructed and made to function, is just a home for the bacteria that keep your fish safe by consuming fishy wastes and rendering them harmless.
The bacteria need a substrate in which to live such as a sponge, gravel or filter wool, as well as oxygen and food from constantly flowing water. If the filter is turned off the bacteria will begine to die.

Set up the tank, add water and plug in the filter - start the filter and throw a couple of pinches of fish flake food into the tank. This will slowly decompose and will provide food for the bacteria until your fish arrive - add another couple of pinches every week, until you have had the system running for three weeks.

DO NOT BUY THE TANK AND FISH AT THE SAME TIME

Use your three weeks to place the plants if you want them, and give them time to settle in.

By now the filter bacteria should be fairly well developed. At this point purchase an ammonia testing kit and a nitrite testing kit. Check for both poisons in the water. If both are zero, you can be resonably sure that the bacteria are functioning well, and it should be safe to get some fish.

Asides from the bacteria, other filtration media, such as carbon, can be added. Be warned that carbon has a limited lifespan and requires regular replacement, so should rather be used for specific purposes.

There are three aspects that I look for in a filter:

(a) Efficiency

For me this requires a motor-driven filter as they act on the water directly via an impeller and can hence move large amounts of water through the filter medium very quickly.

(b) Easy Maintenance

This has to be some form of external filter, to avoid mucking about inside the tank more than needed.
* If you define easy maintenance as that done once a month or so then I would suggest a cannister filter, as they usually have the ability to host vast amounts of filter material. However, they can be complicated to work with, and expensive.
* The filterbox that hangs on the outside of the tank needs maintenance more often - around every 2 weeks or so - but is simple to use and to clean, and cheaper than the cannister.

(c) Low Noise Level

Any air-driven filter needs an air pump and they are all noisy - no matter what the packaging says ! Get a motor-powered filter to keep things quiet - these emit merely a slight hum, which is fine even in a bedroom.

I personally use a motor-powered filterbox that hangs on the outside of the tank - the manufacturer has provided space for 3 units of media, and indeed it usually comes with a sponge and a carbon insert. I then buy 2 more sponges (keeping the carbon for when I might possibly want to remove medicine) and rotate the 3 sponges, top moving to the bottom, and the bottom and middle ones get washed out. This way I always have one sponge that contains fully active filter bacteria

Ideally you should also make sure to wash the sponges in water taken from the fish tank itself, rather than under the tap - thereby keeping a good portion of the bacteria alive in the sponge, while removing the detritus.

Note - When cleaning the filter, especially in those where the water flows past the impeller before getting to the filter media, remember to clean the impeller and the place where it fits - I use ear buds for this purpose. Should you find the motor will not start, dirt in this area is often the reason.

One final comment: the Undergravel filter. This is often offered as part of a start-up kit. The filter is generally air-powered so will be inefficient and noisy. Should you really want to go this route get one powerhead for each uplift tube (a powerhead is an electric motor designed to fit into the uplift tubes of undergravel filters) - An uplift tube is a vertical tube that moves water from the base of the filter plate to the water surface, thereby causing water to flow through the gravel where the filter bacteria reside.
You will want to ensure you have sufficient gravel to maintain a depth of 7 centimetres across the whole tank. Also be warned that plant roots impede the water flow, as do rocks etc - if you want a heavily planted tank, go for an external filter.
You will need to vaccuum the gravel to remove detritus and this should be done as part of the water changes - see the section on water for more info.