What should I use to build a parrilla?
What I would do: 

Buy a grate that is mean for a grill that is the size you are making your parrilla. Usually you can find square cast iron grates for not too expensive and if you need a bigger surface, design your grill in multiplies of the size grate you choose. 

You haven't mentioned the brick work, but make sure you use fire bricks for anything that will be exposed to the heat of the grill.