In terms of small arms, the Iraqi Army is being equipped with AK-47s, RPK machine guns, RPGs, etc. Soviet-bloc weapons that they're used to and are reliable in that kind of environment. They're also cheap to aquire, making it easier on the Iraqi economy.
Armor and aircraft however, I'm not so sure about. The question is if they'll go with Russian tanks and fighters or if they'll follow the example of the Saudis and scrap them in favor of American M1 Abrams and F-15 Eagles. That's what I would do if I was the Iraqi government, especially since I'm pretty sure that the US military would supply them at low cost. The F-15s would go fast, with the F/A-22 Raptor now beginning to be phased into US Air Force active duty squadron service.