The larger the wire size for 'n' turns on an iron core the more powerful the magnetic field will be. It will also demand more current from your power source.
I hesitate to say that another member is mistaken, but the thickness of the wire has no direct effect on the magnetising force. Apologies, Chris!
If a fairly technical discussion suits you, try:
http://en.wikipedia.org/wiki/Electromagnet
Otherwise, magnetic force is proportional to N*I. N is the number of turns of wire wrapped around the core, and I is the amount of current. So doubling the number of turns, or doubling the amount of current in the wire, will double the strength of the magnet.
However! There is a limit to the strength of an electromagnet wrapped around a core, and that limit is the amount of magnetic flux which the material will carry.
It might sound tempting to try a magnet with no core whatever, but free space is not a good 'conductor" of magnetic flux, so vast currents and impossible numbers of turns would be required to get much strength.
Mark