Forget the window, pussy. They don't extract anywhere well enough for kitchens. Building Regs ask for a minimum 30 litres per second extractor, but you aren't obliged to fit one with a simple kitchen replacement.
If you have a gas hob, then you'd be very foolish to have no overhead extraction. Even without gas (which forms water as it burns). cooking sends a load of water vapour around the house. Then there will be condensation problems.
Simple charcoal cooker filters are only good for smells. You really do need either a fan driven cooker hood ducted to outside, or a ceiling/wall mounted fan.