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Where to incorporate for 100% privacy and bitcoin business?

I would recommend you to first check where your business is required to hold a financial service license and where you may operate without. Otherwise you will need to cheat you to a solution like the many other services I have seen do! This will not be a long term business then and you will need to consider to reestablish your business every 3 - 6 months when either PayPal, the Bank or other financial institution close your account!
 
You can do as most are doing it and simply incorporate a Seychelles or Belize company or you do it with a Costa Rica corp. all 3 entities will work for this purpose as long as you stay under the radar and don't tell the bank what you are actually doing!
 
What kind of business are you planning to incorporate Bitcoin with? I've been thinking of setting up my own business in adult niche as well in the future but I don't think PayPal would agree to it. Seems like I'm going Bitcoin all the way if its working with these kind of companies.