IMO flat is the best and knockdown is as dated as popcorn . You do need to realize the mess from removing the popcorn is awful and often the best is to cover it with thin drywall but i think once you cnage those spaces you wall want to do the whole house.

We removed some popcorn from a hallway ceiling and I was amazed with how much brighter and crisper the space looked - I would say get rid of it if you can

Flat ceilings would be my first choice.

Flat ceilings would be my first choice, in particular for a kitchen. Make sure to have that popcorn tested for asbestos, before scraping. I like Patricia's advise for just covering it all over with thin sheets of drywall, and taping and mudding and you are done. A lot of the time, the drywall under popcorn ceilings, doesnt have the best taping and mudding, so you may have a lot of that to get done anyway.