Updating Wordpress to New Revision

I'm behind in times. I started building Bows.com with very little Wordpress knowledge. I'm using Classipress from Appthemes just for the CMS backend. I have a Child Theme installed as well. My issue is, I haven't had a chance to work on the site since early last year and I'm on 4.3 so really need to get this done. I have a backup site which I can make changes to so I can run tests. Is this something you can help with? Thank you.