I don't know who should rebuild the oil fields...but some good old Yankee ingenuity might be better in the long run than unknowns...how could Iraqis deal with that plus nation building plus trying to keep down various tribal factions etc....the oil has to keep flowing and flow faster for the best interest of the country and the world. At the same time, I don't think anyone but Iraqis should get the contracts for the more mundane projects...the schools and hospitals and at least some of the roads etc...
And one of the first things they should do or we should insist on, despite the fact we are piss poor in our own country at this, is developing or renewing if they already have it, a system of vocational education that not only trains the young people but the workers who have been displaced for so many years. Start with the construction trades and the medical trades and go from there.