Flat ceilings can be the hardest and most expensive drywall ceiling finish to achieve but is recommended in kitchen and bathrooms because it is less likely to collect grease and grime. The reason it is more expensive is because it requires more coats of drywall compound to make it look flat. Textured ceilings are used to cover up any imperfections in the drywall finishing process. Be sure to paint these ceilings with a quality flat paint to help hide shadows and reflections from imperfections.
Popcorn ceilings are the cheapest texture to apply to cover up the ceiling imperfections. It is also easier to repair. Small repairs can be done with a spray can from your local hardware store but larger repairs may be easier to spray the entire room. Popcorn ceilings collect a lot of dust and grim and can't be cleaned easily. Many people paint their popcorn ceilings using a heavy roller but since the material is waterbased, you can easily pull it off creating a bigger mess. Some people avoid this by using oil based paint. To remove an unpainted popcorn ceiling you can wet it and remove it with a putty knife. Give it a good skim coat and sand and you can have a nice flat ceiling. Painted popcorn ceilings require dry scraping and sanding, along with a few coats of compound.
Knock Down ceilings or California ceilings are very popular these days because it is a much better look and covers up the drywall imperfections. It collects less dust and can be easily painted compared to popcorn. It can be easier to make it into a flat ceiling by just giving it a coat or 2 of drywall compound and sand. It is, however, very difficult to make a patch in because there are so many variables in how it is applied and often hard to replicate. Often a entire room redo is required to hide a patch.
A bonus ceiling is called a "splatter" ceiling. It is basically knock down finish with out the knock down. They just spray mud on the ceiling. It is used for ceilings that are not good enough for knock down but do not want popcorn.
Make sure you always have good ventilation to help keep the ceilings clean. Make sure you use your range hood when cooking and bathroom fan when showering and leave it on for 20 minutes when you are done. There are fan timers and moisture sensor switches you can buy for your bathroom fan to make life easier.