Uh, for what parts? There's at least three important ones I can think of: core, bobbin, winding.
I think it's pretty clear the core needs to be made from some iron alloy (electrical steel), and the winding needs to be made from copper (minimum size) or aluminum (minimum weight/cost).
As far as efficiency (magnetic flux density and volume per power input), there is only one way to save massively, and that's by putting in a hard magnet. Or, I guess, supercooling everything, preferably using superconducting wire -- but, that's a rather more expensive proposition.
You don't say what parameters are open to design at this stage, nor what budget, or material selection (other than a non-exhaustive list of possibilities), or even what specifications are (beyond generally being big?), so, there's not a whole lot to go on here. For example, we can't even determine if mild steel might in fact be sufficient; Bsat tends to be lower than proper alloys (not to mention magnetic hardness), but if say 0.6-0.9T is enough, why not, right?
Tim