You have web-hosting at your disposal and obviously a degree of web/software related skill, so you don't need the less capable 'hold your hand for you' freebie services.
Dedicated open source software is plenty good enough, and I'd add my endorsement for CMS (content management systems) software such as WordPress and Joomla!, both of which have excellent back ends, plenty of templates available to modify to your needs, and plenty of plug-ins available for a wide range of purposes and facilities. (I can't comment on Drupal because I haven't used it.)
WordPress default installs as a basic Blog site, as it is specifically tailored to such purposes. Joomla! default installs as a more comprehensive web site, with menu and news thumbnail front page, so you'd need to disable numerous features and use a dedicated blogging plugin with it. Despite that my personal preference would be Joomla!, because I believe that its admin/management console is more sophisticated, flexible, and easy to use. Most folk though, I feel, would recommend WordPress instead.