I have experience at several companies testing website variations. What you are looking to do is commonly called split or A/B testing. There are several companies that provide split testing services.

My favorite testing tool is called Optimizely. (https://www.optimizely.com/plans/#testing). It has free and paid plans depending on your needs. The tool has a lot of engineering going into it, meaning it probably won't mess with any other analytic services you might have on your site.

I have used split testing solutions that caused Google Analytics and other tools to incorrectly pick up data. If you are using any scripts or third party services on your site, it is very important to make sure split tests do not interfere with them.

Optimizely will allow you to test different pages or even minor alterations to the same page. You can make these modifications using a powerful editor that requires little coding knowledge.

Before you setup a test, you must make sure Optimizely is tracking the right goals. Goals are any interactions that indicate the test was a success or failure. You can track specific clicks on the page and whether other pages were visited.

After enough people have visited your test, you may reach statistical significance. Statistical significance means the sample size of people in the test was large enough to be reasonably sure the winner didn't win by pure chance.

The hard part about split testing comes when you can't reach statistical significance or can't make sense of your results. That is where a conversion rate optimization expert or growth engineer can help give advice on next steps.