What's the most important factor in determining an elements place in the periodic table?

Probably its atomic number (proton number), because this is how they are arranged already.

Other factors are their form (metal/non-metal) etc., which determines how they react with each other and bond.

Another important factor is the number of electrons in their valent (outer) shell. This is because it tells use how the atom will react/bond with other atoms, how 'violent' that reaction will be, and whether it will bond at all (eg. nobel gases)