I would not recommend self-hosting WordPress unless you’re willing to be very on top of security updates. WordPress is the most widely installed web platform in the world, and as such is a very common target for attacks and exploits. If you keep on top of your updates you’ll do fine, but as security updates are released, the vulnerabilities are announced, which gives attackers knowledge of what they can use against installations not yet updated.
Even if you are not storing any sensitive information, your install can be harnessed for link farming, use in a botnet, hosting illicit code, etc.
WordPress itself will host you with a custom domain for $5 a month. If you go the WordPress route, I would recommend this option.