read up on threat models, and how they apply to online security. Basically, what threat are you defending against, and what can they do to you? Are you protecting against your neighbor who's of normal skill but is just a bit nosy? Do you live next door to the hateful version of the lock picking lawyer that has a vendetta against you? Are you torrenting Disney movies? Are you Edward Snowden and the CIA's trying to find you in the continental US? Or are you in Hong Kong already, or are they already camped across the street? Is Mossad after you for some reason?
All those are different threats, of different sophistication, with different ways and things to protect yourself against. If your average neighbor's just a bit nosy, encrypting your WiFi with a strong password with wpa2 or 3 is sufficiently. If they're a motivated attacker with an advanced skill set, then either 802.11X, or go wired-only for using the Internet. If you're torrenting movies in contravention of copyright laws, use a VPN. Any one, really. If, however, you're trying to defend against the CIA, You can't trust any VPN to protect you, you can't even really trust Tor to protect you. And if you're trying to protect against Mossad, you're already dead.
Take that modeling and apply it to your concerns. What is the worst Google is going to do to you with everything they have on you aka your search history? Take steps to prevent that. Incognito mode, using a VPN, different browser, clean cookies; go to whatever lengths you deem necessary to protect yourself against the threat they pose to you, and if you could wind up behind bars if you Google for "how to get away with murder" and then kill your spouse. (I mean, don't kill your spouse unless they're trying to kill you, but it's a true story.)