I've been optimizing a large SaaS website for a few years now and found that the biggest gains were on the payment pages and pricing pages at the end of the funnel.

That being said, for this particular site, there were glaring usability issues with the site and poor content on the pages so it was the obvious choice of a place to start.

To find places that you can make the biggest impact, after you've fixed any glaring usability issues, look in Google Analytics for pages with high exit rate percentages. These are pages that people had issues, if you can answer their objections then you're one step closer to a conversion.

If you'd like advice specifically tailored to your website I'd be happy to help. Give me a call here - https://clarity.fm/domlinder

1. Be clear about the benefits of your product. It's so easy to talk about features, but if you can translate those features into real benefits for your users then you're words will be more effective.

2. Continue the conversation from whatever source brought them to the site. Ensure that you are matching the message that brought them to the site. E.g. If I click on something that says, "Free Painting Tutorials" I don't want to land on a page selling artist materials.

3. Understand who your users are and what motivates them. This will help you know why your users like or dislike parts of your website and services. Qualitative research (surveys + user testing) will help you to gather this info.

4. Answer objections. Once you know who your target users are create content to answer all the objections they may have.

5. Have a clear funnel for your website visitors to follow towards a conversion goal.

6. Optimize.
a. Find pages with high exit rates in that funnel.
b. Run user tests to figure out what their objections are and why they might leave the site.
c. Tweak the content and copy based on research.
d. Run tests, or simply monitor results, to see if things improvement.

If you'd like advice specifically tailored to your website I'd be happy to help. - https://clarity.fm/domlinder

Redesigning a site won't affect your ranking in the search engine results pages (SERPs) if you do the following:

1) Keep the same domain name.
2) Use 301 redirects to your new pages if you have renamed them or added content. (Example: your old page was at "www.example.com/what-we-do" and your new one is "www.example.com/services".)

To do a 301 redirect on a Linux server you need to edit your .htaccess file in the root directory where you site is hosted. The simplest redirects, just pointing an old page to a new one, look like this:
"Redirect 301 /oldfile.html /newfile.html"
(with no quotes and one redirect per line)

-- Prototype --
I would add that you can create prototypes more simply by just using static images and adding interactive elements to them. I recently discovered MarvelApp (https://marvelapp.com) and you can create mobile + web prototypes for free with them. I would recommend hiring a designer to make the prototype look impressive if you have the funds.

-- Messaging --
On your site you want to be clear about the problem you are solving or the benefit you are providing to make people's lives better. Answer the question - Who can't live without your product?

If you have a target audience in mind, provide examples of how your product would integrate into their daily life. Provide examples and try to be as concrete as possible.

If there are other big names doing something similar to you - mention how you are different and superior so they can frame your product in their minds.

-- Traffic --
I think Andrés' ideas on getting traffic to your site are great. I would add Google Adwords or Bing Ads to the list if you have some cash to play with. In addition to bringing more traffic, this is a great way to test out which wording resonates with users the most so that you can use it on your site. Online Ads also let you play with targeting different demographics to see where you get the most interest from.