It's up to you and how far you want to take the restoration, budget, etc.

If this is something that you are just looking to get done as cheap as possible, then re-using the braid and sockets is the way to go. A small flat head screwdriver will pull out most staples without a lot of effort. If this is going to be a nicer restoration and you plan to keep this in your collection then I would definitely replace the braid and sockets with new.

In my recent pf swap I used this braid (bare wire by the foot). It is very high quality:
http://www.pinrestore.com/Supplies.html

For the staples I used this gun and these staples from Amazon:
Gun- https://www.amazon.com/gp/product/B000N52KSW/ref=ppx_yo_dt_b_search_asin_image
Staples- https://www.amazon.com/gp/product/B00002267U/ref=ppx_yo_dt_b_search_asin_image

44 lamp sockets are available from all of the major suppliers.

There are a lot of threads on Pinside to help with the swap. Good luck!