No need for brake cleaner unless you get grease/oil on the shoes when you are done. As said before, remove all wheels for a complete inspection.
Emery cloth is good to clean the glaze off the shoes. Just like buffing your shoes after you polish them, if you have ever done that. Not many shoes are real leather anymore.
I would change/flush the brake lines. The brake fluid absorbs water and is at least 5 years old. Moisture corrodes the lines and wheel cylinder from the inside out, so you can't see it unless you flush the fluid out. A quart is less than $10. Only se a new, sealed bottle. Old brake fluid, previously opened fluid should be tossedd
On this car you would start at farthest wheel from the master cylinder and work back from there. The passenger right rear and work back.
Your Factory Service Manual will give you the correct brake adjustment procedure.