Updating versions, Plugins, and

First time post – Complicated (I think) Hope someone as thoughts.

Overview

• A third party vendor managing Google PPC built the site, then left this WP version at 3.7 (I believe, cause they have all their own version put in so hard to tell for sure).
• I’d like to move up to 4.2.2, but I have heard nightmares and do not want to break the sight and have to start over.
• It has Yoast SEO 1.47, but I want to update that to the latest as well.
  It doesn’t not have Yoast GA plugin, but I want to put that in as well, however it says I need at least WP 3.8 and apparently best guess I have is 3.7 (that’s the latest license I see).
• Finally it was build with built with the WP theme Ultimatum.

I usually start from scratch, so I have not had to deal with so many updates, but I don’t have the option this time. So I’m looking for answers or suggestions.

Thinking

• I could copy the entire site.
• Update it to 4.2.2.
• Update Yoast SEO
• Add Yoast GA
• Pray it all works

Make sense?
Suggestions?
Questions?

Or do I just start all over over and honestly that former 3rd party vendor has not been forth coming with a lot of info, like I cannot really tell what version of Ultimatum that they’ve been running.

Also, If I didn’t ask question correctly, I can learn.

Thanks in advance