Do they work as well as the hang-on filters?
Hang on filters usually have more capacity. This means they can hold more benificial bacteria and remove more solid particles from the water, provided they have the right media in them. So in short, yes, most HOB filters are better than internals.
Can anyone recommend good and reliable brands and models?
No sorry but if you're really keen on brands, stick with the ones you know.
If we have an internal filter, do we need an air pump as well, or do they provide enough surface agitation on their own?
Dependant on where you put the outlet pipe, they can produce enough surface agitation. You may wish to add an air pump if there are no plants in the aquarium or fish appear to be suffering from lack of oxygen
Our tank is only 60L and currently very understocked, but I'm not sure how to work out what size filter we need, and I presume it is better to get one a bit big than one that is only just big enough?
The general rule is to get a filter that can filter your tank's capacity at least 6 times an hour. This means you'd need a filter that moves 360lph prefferably more because the media will get clogged quite quickly.
Hope that helped