While the above have merits, the simple way to backup your entire site including database is a free plugin from wordpress.org called duplicator. This plugin will backup - Database ( including user and passwords ), posts, images,comments, videos, settings,plugins ( including all settings ),users,comments,ads, traffic stats, themes, child themes. So in fact the duplicator plugin will save absolutely everything. Then from inside your admin you create a package zip file and download to your desktop. You can then move your entire site including database etc to another host in minutes or keep a complete backup ready to install if anything goes wrong with your site. I use this plugin on all my sites from big ones with hundreds of posts to new sites. I use this to install sites i flip which can be installed on a new host within minutes. So no need to contact hosts, dump databases, just a very simple plugin and you are good to go