You can get away without a database (and assuming you don’t need anything too complicated, I recommend not using one). I’ve had a good experience with GetSimple - it’s a content management system (like WordPress) but uses regular files instead of a database. Great for basic content, and still easy to set up and manage.
Self-hosting is a bit complicated if you’re not already comfortable running a Linux server. Not sure about privacy (though I’m not sure how privacy intersects a public-facing website), but there are lots of hosting providers out there. I use DreamHost and have had a great experience there.
You might also enjoy a selection from Hark, a Vagrant.