My personal method would be whilst in one piece would to if possible steam clean the whole car with the engine running as this will save a lot of time later, then spray wd40 or whatever you have, even diesel would do on every nut and bolt that you are going to undo.
Take off only what you need when you need to save time and reduce the chance of loosing something. The rest on ebay or offer on one of the MX5 forums and get some cash back.
Good luck with your build and enjoy.
