You can always save backups to your own computer...
And if you rent server, I mean
server or even virtual server, it means that you got server which you can manage as you which, install mysql server, www server and what ever you want to.
e. Of course own server box in home is nice, cause it's easier to control, but usually if you rent server it comes with 99.9% uptime and stable connection and so on..:d