Is there a reason to not use google's DNS servers?
Solution 1:
Are you aware that using a VPN means that you are trusting the VPN company instead of Google? Although the voracity of Google to gather private information is astounding, I don't believe they'll be able to connect everything you do into a package.
You can increase your privacy by logging out of your Google accounts when you research stuff, change your finger prints (different browsers with different user agents), browsing in private more, removing cookies, and much more.