APPle Macbook pro (about 4 or 5 years old) question.

I am a senior citizen and i worked with computers when I was working back before
2002..but Now I get a little confused??? I get this notice quick frequently - and I have been using Safari. I like it...because it is familiar, so if anyone can help me without me
calling in some geek for $50 bucks an hour, I would truly appreciate it.
On a desktop computers years back I used Firefox (I believe that was the name)
When I select SAFARI...I get about 9 or so that I can choose from?
That is my dilemma..so far..

Outdated Browser Version: You are using an outdated browser version. Some features on our website may not be available. To get the most out of our website, we recommend you upgrade to the latest version of Chrome, Safari, Firefox or Internet Explorer.
Thanks in advance..
Penny
Kansas City are