Here is the reality. Some developers will try and tell their client not to use this or that, simply so they can design and develop what they want to custom build. What happens is that backs the client into being stuck with a custom developed website, and when that designer/developer moves on, it becomes very difficult for the business owner to then manage the ongoing design and maintenance of a website.
There is a very good reason we buy popular cars off the production line and don't custom build cars by hand. Because they are popular, there are many places to get service and there are many technicians who are trained in servicing those products. When you choose a CMS like WordPress, you then have at your disposal an incredible amount of resources to support your site. Backing yourself into a custom build is nonsensical for any business owner. And, I can't imagine that a graphic designer is going to design any template that will not be adaptable to WordPress.
When one thinks about WordPress, one can't assume that since they see this WordPress site or that Wordpress site, their site can't look any different. There are millions of WordPress sites on the web - many custom sites you've probably never seen or never will see. And, why do you care to design something that is not standardized for your industry? As an information architect, I will tell you that we have web standards for a reason. To try and change the layout of pre-established and successful guidelines is to confuse the people you care about the most - your customers.
Lastly, when you use WordPress, it becomes very simple to login and edit page content, without having to hire a designer or developer to add or update your content and push it via FTP up to your webserver. If you are going to have a "news" feed, what do you think is going to run this news feed? That's basically your WordPress blog engine that publishes your posts in reverse chron with categories, tags, and the ability to add comments. You really want to custom build a website with a post-generator engine to publish new news posts and add all the ancillary tools that already exist with WordPress? If something has already been done and done as well as anyone has ever done it, what do you think is going to be so different?
It sounds to me like you have no experience in web development and are listening to someone who wants you to write a big check to do something that, as a business owner, you have very little understanding of.
Let's also talk about your careers page. I built a website for mks-corp.com in Boston and installed a careers plugin to post jobs with an experiation date and the ability for potential hires to apply online and upload their resume. Do you know how much that costs to build from scratch? Just the form and upload tool alone would take many hours to design and build, but you can get a plugin to do that for $50 and you're on your way.
You say you want a blog. WordPress is the MOST POPULAR BLOG SOFTWARE oin the world. WordPress.com powers millions of blogs. What would you use then? How would you create a sitemap and register it with Google Webmaster Tools and make sure your site is SEO ready by having disparate elements tied together, quite possibly with subdomains.
Every time I go back up to read your post and reflect, then write here in this box, it makes me increasingly angry that someone has given you such horrific advice. I've worked in software development since 1995, am an accomplished vp of product, have run my own startups, advise other startups, and am a digital strategy coach. What would I do? Fire the person who advised me to do something so foolish and hire someone competent to get the job done with the available tools that keep your costs in check and will get you online in months and not years.
And, one of my clients is NurseCall.com, a software company that has a primarily static marketing website. They are extremely happy with their WordPress site, which is well SEO'd and does everything they need it to do.
I urge you to rethink this. If you want custom design, then hire an experienced WordPress designer and front end developer. If you need some advanced logic for cool stuff that node.js or backbone.js can do, that's great, but you probably don't even know what that is yet until someone shows you what those technologies can do.
I wish you the best of luck. If you don't choose a CMS and build this project from scratch, then you're in for cycles and cycles of development and dealing with problems that WordPres and all its third party plugins handle already.