As chem says the freq is important, silicon steel presuming thats what your using has a freq limit, and you mention pulses so freq could be high.
Whenever I design or choose an inductor out the junkbox saturation current is an important consideration, and the cross sectional area is one of the most important fators affecting saturation, the higher the csa the lower the core flux density is, and the greater the current the inductor can handle (as a rule).
You can use the universal transformer equation to calculate flux density within the core, silicon steel from memory can withstand 1 Tesla, ferrites aroun 0.1 to 0.3 Tesla.
The closeness of the windings to the core affects coupling, leakage inductance and other parasitics, this can get complicated, keep the windings as close as you can.
The guage of the wire affects the current carrying capacity of the inductor, there are diffrent rules of thumb, on ebeing current density, if you keep density less than 4a/mm2 you should be ok at freqs below 300kc.