While I agree that Eheim is probably the best brand in terms of reliability and longevity, I'd take issue with the comment that undergravel filters can't work well. They can work exceedingly well, and in terms of biological filtration are excellent. They do have shortcomings though, and these are why they are less commonly used today than previously. Specifically, they don't work with plants that have roots in the substrate (they're fine with floating plants and epiphytes) and they only work well in tanks that have minimal amounts of rock or bogwood. Undergravel filters don't process solid waste well, so with big fish, you can end up with lots of faeces and silt about the tank. Such waste isn't dangerous, but it looks horrible.
Undergravel filters do have one great advantage though: for the price, they're very effective. If you're on a tight budget, it's hard to beat an undergravel filter with an airstone or powerhead at each end of the tank. Do make sure you maintain the gravel properly by stirring it once a month (at least) and siphon off any silt you find. Also avoid creating too many dead spots under rocks and bogwood, and also ensure the gravel bed is evenly spread out across the tank, otherwise the water will take the path of least resistance through the shallowest part of the bed (which is why digging cichlids can't be kept with undergravel filters).
Why are they so good for the price? Because they -- by definition -- circulate oxygenated water through the bottom levels of the tank, ensuring a good distribution of heat and oxygen. They also have a massive surface area on which bacteria can grow, and because they bacteria are exposed to the water in the tank, if there is little risk of the bacteria dying during a power outage (as happens within half an hour in an external canister filter). Obviously the gravel is cheap to buy, so setting one up isn't expensive.
Do understand that when you see a canister filter or hang-on-the-back filter advertised as being "suitable for 20 gallons" or whatever, that's a generous estimate. Manufacturers assume the best case scenario, in much the same way as motor manufacturers when they tell you your car does 35 miles to the gallon. Yes, it may well do, immediately after servicing, downhill, with a following breeze, no traffic lights, and not carrying any passengers or shopping! I prefer to recommend people buy filters based on turnover, with a minimum turnover of 4 times the volume of the tank per hour recommended for small community species like guppies and neons. In other words, for a 20 gallon tank, you'd choose a filter rated at 4 x 20 = 80 gallons per hour. Bigger fish like goldfish and cichlids need proportionally more, I'd say 6-8 times the volume of the tank, minimum.
By contrast, undergravel filters almost by definition scale up and down with the tank in question. So you can reasonably expect the undergravel filter in your tank to be adequate to the needs of any small community fish being kept. With bigger fish, the "reverse flow undergravel filter" is recommended, and in many ways this is one of the best filters available, period.
Cheers, Neale
Welcome to the forum. I've always preferred the external canister system. The brand I use for both heater and filter is Eheim, though some can be a bit pricey. I wouldn't use an undergravel filter if I were you. They just don't work as well other filters. Plus with an external canister filter you can adjust your spray bar to create suface aggitation which will help with oxygenization.