If I build an intelligent construct and pay to add HD to it....

[metabolicjosh]

Does the construct gain only racial HD? If so, is there a way to create constructs with class levels?

[AOKost]

I believe you can indeed create a construct that is intelligent, but in doing so you must create it with as many HD as you want it to have upon creation. After that, it can choose to gain a class, or to improve itself by gaining Racial HD much like a monstrous racial class.

[Abd al-Azrad]

I would recommend the Terra Cotta Warrior. Intelligent construct, with a few feats and RHD of its own, which you can customize as you see fit. They also gain combat bonuses when working as a group.