what core material makes for a strong electromagnet?

Answer 1

Ferromagnetic. The cheapest is low iron or low-carbon steel. AC magnets need a softer (fully annealed) iron core for the lowest residual magnetism. DC or DC-pulsed magnets (no need to alter polarity) can use a more readily available low-carbon steel. You may want to use stack of thin sheets that are coatted by a thermally conductive but electrically insulated polymer to block the Eddy current if heat or efficiency is an issue.

Answer 2

soft iron is the material! steel isnot used as it becomes a permanent magnent once wrapped in form of a solenoid.