Here's my take on filters...
Undergravel filters
Good: Cheap to set up. Support lots of bacteria, and if built properly, very effective. Low maintenance (stir gravel before each water change). Reliable (not much to go wrong). Works in any size aquarium and with any size fish (though not necessarily the ideal for, say, red tail catfish).
Bad: Plants with roots don't like them. Limits your choice of substrates. Dead areas under rocks/bogwood. Solid wastes aren't "sucked away", they stay in the tank, which is unsightly. Once a year the filter plate will need cleaning, which involves emptying the tank.
Internal air-powered filters
Good: Cheap. Work well with fry and other small fish. Very easy to clean.
Bad: Limited flow of water, so not much use with messy fish or in big tanks.
Internal canister filters
Good: Convenient. Easy to maintain. Different sizes suitable for different sized tanks.
Bad: Expensive for what they do (poor water turnover per unit money). Lack of water flow limits value in big tanks.
External canister filters
Good: Good value (water turnover per unit money). High pressure water flow, so good for big tanks/messy fish.
Bad: A dog to maintain. Leaks are disastrous. Closed chamber makes them very sensitive to water flow stoppages (lack of oxygen kills bacteria).
External hang-on filters
Good: Open design lets in oxygen for good biological filtration. Various sizes available for different sized tanks. Easy to maintain.
Bad: Fairly expensive for what they do (water turnover per unit money). Limited flow of water so not good for big tanks/messy fish.
These are the basic filter types, anyway. So what you need to do is rank what's important for you. If you have big fish, then external canisters and to a lesser degree undergravels are the best. If you have small fish in a small tank, then an air-powered sponge or an internal canister might be suitable. If you want to save money, then avoid internal and hang-on filters, and look at undergravels and external canisters. If you want something easy to look after, then air-powered and internal canisters have the edge. If you want plants, avoid undergravels. And so on.
Cheers,
Neale