I quite often brew on a Saturday and serve the following Friday.
English running beer is what you are after - ordinary bitter, London brown ale, milds, sweet stouts, etc..
Both Windsor and Nottingham yeasts can finish by Wednesday - Windsor finishes before Nottingham but doesn't ferment as dry.
Two sachets of dry yeast for 20 litres does the trick. I ferment at around 18°C.
Rack into a keg Wednesday night and chill. Carbonate (and dry hop) Thursday night and serve on Friday night.
The beer may be a little hazy - ceramic mugs help - but fresh beer tastes great.