variable regulation source
Every Load has its recommended applied power. Some works by applying AC voltage and other works by applying DC voltages. First you have to determine which coil you will use to know its applicable Amp, Voltage. you want it to be 50 Watt so you have to choose a coil that consume V(voltage) x I(current) = 50 watts. Also you have mentioned that your regulation source is going to work only for supplying the heating element of the soldering wire "Coil". why you are going to use a variable regulation source? to learn how to design your regulation source refere to the following links.

Basic Power Supply Application Guide

How to design and build a linear power supply

How to design a regulated power supply