How to properly wind coils for a solenoid?
Windings that are side by side that carry current in opposite directions cancel each others magnetic field - you need to wind the electromagnet so that current travels in the same direction in all turns of the coil. There is no sensible argument for doing differently.

The strength of the magnetic field is related to number of turns and ampere's flowing. For the same number of turns wound on a longer solenoid the field reduces with solenoid length.

These are your only options other than to use superconductors! Fewer turns can be compensated by greater current or reduced solenoid length (stacking turns).

Here's a calculator you can use to estimate field strength and it uses a field value called permeability and this means you can check on various materials and choose one that gives the highest strength BUT for household coil making a piece of iron is fine.

You can also enter the diameter of the coil.