Hey Robert,
welcome to the forum; there is no fixed order, but it is wise to slowly build up to Everest by learning on all aspects of that climb: altitude, technique, cold etc.
See also
this FAQ. Most people do either Elbrus or Aconcagua after Kili, and then work their way up Vinson/Denali until they get to Everest in the end.
Kosciuszko can be done whenever you are in the area and have a day off, Carstensz needs high altitude rock climbing experience.
Do not underestimate the step from Kili to Aconcagua, though technically not much harder, Aconcagua is a different ballgame...
Best is to take loads of courses (in the Scottish highlands for example

) and go on a longer and higher expedition each year as well.
