How to back up site and whether to update plug ins and theme

A developer created my site and I do not think it is backed up anywhere. I have made many updates since it was created so I would like to back up this new version of the site. How and where do I do this?
Also, the dashboard indicates I have 10 updates waiting...wordpress 4.0, and some plug-in updates and maybe a them update. I am afraid to update anything incase it screws up the site. Can someone from your support staff take a look at what is necessary and safe to update? Thank you in advance.