Replace the cables & chain, rubber & brake pads,bar tpe & saddle if you like.Lube her up and ride it and make sure its a good fit before investing much more. At that point you will have an ideal "beater".
Don't be in such a hurry to replace the headst & stem. It would also require a new fork. To save a couple bucks you could use a threadless adaptor with new stem, original fork & headset.
Good luck, The World Sport should be a nice solid bike, a fun project and a great learning experince.