An exhaust fan in the kitchen is not an absolute necessity. However, it serves two functions: it cuts down on humidity and it removes grease, smoke and odours. If none of these bother you -- and that has a great deal to do with how you like to cook -- then you can get along without one.
If you keep lids on your pots and generally do not generate enough humidity to fog up the kitchen windows, you may want only a range-hood filter to trap the grease and filter the smoke. These vary in the effectiveness, though some very expensive models with charcoal filtering are surprisingly effective.
If you want to get rid of all the excess humidity and pollution then you need to vent outdoors. Range vents should not be run through the Heat Recovery Ventilators because, despite grease filters, they eventually clog the exchangers. A vent from the kitchen, but not over the cooking range can be run through a heat exchanger, particularly when the grease is already trapped by a recirculating range hood filter.
When you are choosing a range hood ventilator, pay attention to the noise. When they are noisy, nobody will turn it on. It costs more for a quite one but you can buy ones that are not even noticeable at the lowest speeds. You can also buy an in-line fan, where the motor is not even in the kitchen and they are quieter yet.