Degreasing is gonna take a while, especially near the oven and hob.
I normally use meths and lots of jay clothes, followed by 240 grit sanding.
I would use household ammonia et al but often I am repainting MDF (shaker style doors) and do not want to deal with the grain swell.
Pre 2010, before they fecked up oil based paints, i would have recommended Satin but these days there is very little difference between satin and eggshell.
I still prefer working with the latter though, creature of habit...
Dont forget to factor in the cost of removing the recessed hinges. Often a day to take off and rehang (the plus being that the doors will probably be out of line now anyway- meaning that you can offer to retweak them). Even if you are not repainting the inside of the doors you will still need to take the doors off to paint the faces of the units. Built in fridges etc might require removing the nylon runner etc.
If the doors are 100% sound then you might want to consider water based. Heavier tramlines (requiring additives such as Floetrol) but less inconvenience for the client. Eg no evil smellls if they try cooking later that evening.
The high end firms often fit the units with acid-cat primer and the onsite decorator uses waterbased. In part, this is so that the client can use the kitchen a couple of days earlier.
As a cabinet painter I have to admit that only 5-10% of waterbased kitchen finishes (that i see in clients homes) impress me, and those that did were real timber rather than MDF anyway, meaning that the tramlines were less obvious.
However you price it, add an extra 15% (at least) on to the final cost. You will understand why afterwards!!!
Good luck