If you only have enough steel for one piece per dwarf, you're probably best off with helmets or breastplates. Shields are even more important for a dwarf's survival, but wooden shields are just as good as steel unless your dwarfs have a habit of swimming in lava (which, you know, happens). Once your dwarf has a shield, most kill shots are to the head or chest, so those are the first things to protect.
Most enemies don't really wear significant armor, so iron or even bronze axes are just fine while your steel supply is limited.
However, if the problem with steel is a lack of fuel, rather than a lack of iron, I would put what little fuel supply you have into building iron pump components. With this you can dig down to find magma, which is much more efficient for creating steel.
Finally, if your limitation is not steel or fuel but armoring expertise, shields are by far the most important armor item. However, wooden shields (which as above are just as good as steel, except against dragons/lava) are made with the carpentry labor, not armoring. So you can split up the labor that way, leaving the armorer to make the more specialized helmets and breastplates.