"The extractor will be over the hob, on a wall that will allow it to vent to the outside. I want it to actually drag any dirty air out, not just the grease."
That's fine. Modern extractor hoods usually have a 125mm or 150mm duct (older ones were 100mm). A larger one can run slower, which makes them quieter, and can be more powerful. A plumber or kitchen fitter will have a core drill which makes a neat round hole in ordinary brick or block walls.
A few tips:
IMO a hood or canopy is best if it is a little wider than your hob, so it can catch fumes that drift slightly sideways
Fit it slightly above head height so that you don't bang into it when leaning over pans
The duct usually comes out of the top, so the hole in the wall has to be higher
I am rather attracted by the ones that build into a canopy disguised as a run of wall cabinets, rather than hoods.
Some are available with a slide-out or fold-out panel that you are supposed to open before you start cooking. People with these never bother to use them properly.
I am very fond of Elica, who make a large range to suit all pockets. Their website is awful, so email them and ask for the glossy catalogue by post to help you choose.
Modern extractors usually have metal mesh grease filters that you can put in the dishwasher to clean. You will not need a carbon filter if you are blowing the fumes outdoors, unless your neighbours complain about the smell. It is possible to have a "chimney" attached to the wall to take the fumes above the roof, but this is rare domestically.
Extractors sold by kitchen companies are usually overpriced rubbish.
The cheapest extractors usually have a low throughput (quoted in litres per minute or cubic metres per hour) and may be noisy. Better ones have a range of speeds (the lowest being very quiet) and often have two fans.