From what I can see it looks to be a real '58...neck pocket shows it was a burst, but correct me if I am wrong it appears to be a 3 tone, I thought the 3 tone came out in the 60's?
If that is the case then it has been refinished at some point in time already other than the strip. So my suggestion to you is go with somone that knows what they are doing and have it refinished in a period correct color that you like. As far as the neck in concerned if you are going to refin might as well refin the neck up to but not including the headstock. I do not care if an instrument is refinished...I buy to play not to just let them sit there and collect dust.