power filter

concept
Power filters are probably the most common filters for aquariums on the market, and they vary in function, size, shape.

But, they all suck in water through a propeller, draw it through filter media and then spit it back out.

in practice
But, the presentation can vary. There are intank, hang-on, waterfall, spray bar, and attachments and adjustments so that maybe you can do any or all of the above.

For a newbie (like me), it is usually a good idea to get a power filter that is rated maybe.. 1.5x to 2x your tank size. The water parameters will be more forgiving and you might have more time between seeing your fish act funny and seeing them die; hopefully enough time so that you can fix whatever is wrong or transport your fish to a quarantine tank (if you have one that is).

in practice - variations
Since my definition for a power filter is very general, I classify a lot of setup methods as power filtration. Hang on, in tank, power heads/pumps with filter media attachments, canisters and sump filters are all technically power filters, but I'll have a separate section for the last two since they are different enough to be worth mentioning in their own articles.

pros 'n cons
Power filters are all very sturdy beasts and are typically the simplest for the beginning aquarist. Most of the considerations for this type of filter deal with convenience.

pros 'n cons - in-tank
In-tank power filters are fully submersible and reside inside the aquarium. Well, obviously, when you clean it you have to haul the whole thing out.

And, since in-tank filters are typically smaller to conserve space in your aquarium, they will need more maintenance because they get clogged faster.

Their compact size and placement flexibility can be an advantage to setups that require a tank to be partially filled or tanks set up with no room for hang on power filters or other methods.

pros 'n cons - hang on
Hang on power filters are typically designed with a waterfall style outtake.

Since many tanks have lids of lighting fixtures, these hang ons are typically placed in the back along the width of the tank. Which means that if your tank is wider, the major flow circulates forward, down and into the intake so that you have a narrower band of good water flow and the outskirts get some flow.

Compensating with a higher flow rate causes something of a dead zone, where the flow is so strong that your fish get shoved out of the area (which actually can be kind of cool as the fish, shrimp or whatever eventually learn how to "ride" the flow).

Feeding can also be irritating with the waterfall, as floating food (and plants, example duckweed) types get pushed under the water and sucked into the filter. There are ways to prevent this like purchasing or making a feeding ring or putting some sort of obstacle in front of the filter intake, but personally, I don't like the additional hassle.

pros 'n cons - powerheads/water pumps
I haven't tried building my own filter with a pump, but I have tried a few powerhead solutions with mixed results.

First, the powerhead solution became a deathtrap for my pond snails (this can be a blessing, but not to me! Love watching those snails crawl around). They would get stuck in intake areas and eventually die. This may be an issue with the particular powerhead that I purchased, but it was annoying.

Second, I couldn't find a lower flow rate powerhead locally, and the powerhead that I eventually purchased was a bit overwhelming in my 20 gallon long. The complete set of attachments make the powerhead a bit too tall to be practical, but I am considering building/buying a small acrylic container or sponge filter setup to try again.

But, the powerhead gave me really good flow rates at customizable angles, and really helped with collecting detritus and debris from the tank.

recommendations
I highly recommend the hang on filters like the Marineland Penguin and Emperor line of products for beginning aquarists. These filters are easy to maintain and do an excellent job filtering and improving water clarity.

The best part about these filters is that even if you find that you need a more custom solution, you can leave the filter running in the tank to help out.