Dr's appointment, NST, and being induced

So today im officially 40 weeks. My doctor told me at my appointment last week that if baby girl wasnt here by this week's appointment they would do a NST and then we would discuss being induced, my appointment is tomorrow.  I really wanted her to come on her own and im honestly terrified of being induced , im not sure why... Maybe all the awful stories ive heard behind being induced with all the pain as i wanted to avoid an epidural. Anyway, i wanted to request being induced on june 1st or 2nd for many reasons. Any suggestions or comments ladies? Should i ask my doctor anything specific or request anything specific? I never even looked into being induced this whole pregnancy because i honestly didnt think id make it to 40 weeks and STILL be waiting on her!