I use a 40w Draper and it does the job just fine. 40w should be enough for most things.
You want to make sure you're using 60/40 lead solder and that you tin the solder head properly else it wont be hot enough. I assume the solder head isnt all black? thats an indication its been too hot previously and may need to be replaced. Youtube some guides on how to tin, makes a world of difference.
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