If you do that, make it public, or else you can get profiled again.

That is the point, If you want to go really private, there is no other to self host on a own server. If not, it's better to use any of the other "normal" search engine with a good reputation. the privacy it has you can check with the services above mencioned., and to repeat until boredom: important to read TOS and PP to avoid surprises. These are legally binding documents, that is, if they do strange things with your data, without specifying it in this texts, a ton of bricks can fall on them with million-dollar complaints.