Hello Mike,
For freshwater fish, the best all-around choice remains a decent external canister filter, just as it was twenty years ago. Indeed, some filters, like the Eheim 2217, are still on sale and represent good value for money. For your tank, either the 2217 or the smaller 2215 would work nicely, depending on the type of fish you're planning to keep.
A good rule of thumb is to choose a filter with at least 4 times the volume of the tank in turnover per hour if you're keeping small fish (neons, guppies, Corydoras, etc.). If you're keeping bigger and messier fish, such as plecs, goldfish or cichlids, then 6x to 8x the volume of the tank will be in order. So assuming your tank contains 125 litres of water, a filter rated at 500 litres per hour would be fine for small tropical fish, or 750-1000 litres per hour for bigger, messier fish.
Carbon (charcoal) is largely obsolete and I recommend against it.* Back in the day, people avoided water changes and the result was aquarium water turned yellow and filled up with organic acids that lowered the pH. Carbon removed these chemicals, keeping the water clearer. But the modern hobby recommends big, regular water changes (25-50% weekly) so you should never get a situation where the water turns yellow. Hence, carbon doesn't do anything useful.
Internal canister filters can be good for small tanks but they're expensive for what they do. They also tend to work poorly in tanks with messy fish. I cannot fathom any reason why hang-on-the-back (HOB) filters are so popular. Apart from the fact they expose the biological media to the air, ensuring the bacteria get lots of oxygen, they're severely compromised in other regards. For example, they lock you into using proprietary media cartridges, often including useless carbon and zeolite ones you don't need. They also have the inlet and the outlet close together, which means poor circulation in the tank. By contrast both external canister filters and undergravel filters ensure good circulation of water throughout the tank.
Undergravel filters can be extremely good value and work brilliantly. The only reason they aren't popular today is that they only work in tanks with a flat gravel substrate, no plants with roots, and no big rocks. If these limitations don't matter, a properly set up undergravel filter is still as good as any.
Cheers, Neale
*Why? Two things: Firstly, it wastes space that could be used by useful media. Secondly, it removes medication, so you'd have to remember to remove it whenever treating your fish. On top of these issues, it has to be replaced every couple of weeks to do its job. If that doesn't appeal, don't bother buying it at all!