Should I get new website designed in CMS or normal HTML?

Not being an expert in Web-Design myself I started with Wordpress for my own site. I was later asked to design a site for a client who liked mine and enquired who ad designed it. I looked at all the options, even Flash which of course people always say avoid. That's a simplistic answer as not all clients priorities are SEO, for them it's a showcase for their work, especially for high end established businesses and for the mobile issue it's fairly simple to have a redirect to a mobile optimised version. There's still a big market in the Flash template marketplace, so despite the downfalls it still seems to be popular in some sectors.
Problem with Wordpress (for me) is just sometimes it's frustrating to truly make them look creative or different - I've looked at literally 100's on the big distributor sites such as Themeforest and bought a handful - some of the sliders don't work on mobiles anyhow and the simpler ones are quite boring. I have a few themes and my favourites are full screen or ones where the background is not restricted to colours with option to upload your own scrolling and responsive, quite a bit of CSS customisation needed but they don't look like typical WP sites and load times are ok as I've not overloaded with plugins (another factor nothing beats html for page loading quite important in some parts of the world) For clients WP sites are overall better I feel as they can login - restricted of course and maintain their own blog element.
I guess the simple answer is a good WP with a versatile quality theme is usually a good option provided there aren't too many plugins and you're located in areas where internet connection is not like here in some parts of Asia. Of course this is from my perspective and it's only my personal opinion. In short -"Horses for Courses"

As @agmccall said, WordPress is a CMS written in PHP and HTML, and therefore it may be possible for you to just get a web developer to convert your existing site to PHP / WordPress (depends on the site however).

I think you will find using WordPress a lot easier than having to edit HTML because you can add new pages and alter your content a lot more easily with WordPress' visual editor. As others have mentioned, there are also plugins that will help you make your site more share-able and SEO friendly but if the content is the problem then converting it to a CMS-based system is not going to be the solution.

Also, you should be aware that keeping your website secure is very important, you will have to ensure that you (or someone else) applies the regular WordPress security updates to your site to keep it safe from external threats (hackers, spammers etc) - it's not hard to do but it has to be done.

Thanks for your feedback. So I have bought the new domain name, set up the Genesis Framework which I already had bought previously. It automatically updated to the latest version. And then I bought another Studio Press Child Theme for under $20, so little cost to start it up.

I think most of the set up is quite easy. The tricky thing is that the sales letter is currently in html format and the formatting and photos don't quite work when cut and paste into the html section of Wordpress. However, it is not too bad a start. I may need to get a web designer to do this and also get the design of the other sections right.

The rest of the sections are mostly text including an articles section, a separate blog. I did have a coder put together an online test originally for the current site. I realize I could either use his Drupal designed work perhaps in a separate folder /onlinetest with the new website or just go with one of the Wordpress Plug-ins I have seen.

I am realizing that I can use a combination of the main Wordpress site but also other types of files for the homepage or even a separate Wordpress installation for other parts of the website e.g. /blog.

Is that normal to use different formats for different sections of the website? Or should I be trying to do everything from within the main single Wordpress installation?

@Karen Blundell and @Valdor Kiebach: I am hoping the Genesis Framework will deal with the security issues.

@Paid Surveys: I don't think I will do 301 redirects as I have read in a couple of places that Google doesn't like this. And to try and keep the sites separate.

The whole website creation was much easier than expected. I also got a couple of logo designs from Fiverr.com which are not bad. So, originally I was expecting to pay hundreds of dollars to set this up but it has been a fraction of that.

I may still need help with design and if I do use html/php/Drupal etc for some sections of the website then that could cost a bit for design.

One thing is for sure, even though I am still getting some sales from the current website, it has fallen even further in the SE rankings. For the latest month of May, according to SEMRush, I am at 3 for May 2013 US SE Traffic, compared to 18 in April 2013 and 710 back in December 2011.

I will look at other forms of traffic as well such as PR and also Google AdWords and other paid advertising for the new website but essentially keep them separate.