For cores it is best in my experience to use Fiberglass, Carbon Fiber, or Kitespar. In general a half inch diameter for single hand swords and larger diameters for 2 handed weapons.
For foam most big manufacturers use a 1.5lb to 2.2lb density cross linked polyethylene foam tube. The foam can be purchased in planks. Non crosslinked polyethylene is often used as a base for shields and added layers of Minicel are utilized as a final surface for plastidip projects. Camp mat it a POlyolefin foam in a ~2lb density. Puzzle mat foam is a high density eva foam. Most foams used in crafting can be purchased from FoamByMail. Finished tubes are sold by some merchants.
Next you will need some tape for your swords. You can use Tyvek or Packing tape to cover the foam. Strapping tape is used to cover the tip of the core and to secure foam to the core. Next you will need cloth tape for covering courtesy padding or handles. Depending on your specific methods you may also need double sided carpet tape.
For covers I like to use Ripstop Nylon. I have found 2 that I like so far.