This isn’t a trick question, or is it…? It used to be much easier to answer it. Back in early 2000 when web design reality was situated around ‘Is that person capable of creating a website?’ rather than ‘Is that person capable of designing a beautiful website, that is functional and makes people buy products?’ And it is an important matter especially when you're considering who should design your professional business website.
Developing websites in the past
In the past, knowing how to code was necessary. Without understanding HTML or flash, you could not build a website. There was no question about whom should you hire to design it. The problem was that tech people were not known for their exquisite sense of visual style. Making a professional business website that looks good was not a priority if it's appearance was considered at all. You can see for yourself by visiting the Wayback Machine to see how the internet looked like back in 2005! Very few heard of good UI (User Interface) or UX (User Experience). These words may sound silly to a "full-stack-web-developer-engineer” however, now coding skills are not necessary just put a functional website up.
Cheap Websites (or "web design on a budget")
Which is not to say skilled coders and web developers aren't necessary. Not at all! The "no-coding" approach works if we think about a general site, with a basic purpose like displaying simple information. Having an online space that functions as a visual business card or a leaflet is useful to describe and promote your company quickly. And there is a rapidly growing market for that type of web design. The reason? A website is often the first thing your potential customers will look for when they want to learn more about the product or service that you sell. So, you won't get away with not having a website. At least not if you want to appear as a forward-thinking business owner.
If you need to outsource the creation of this type of website, an experienced graphic artist should be enough allowing you to save some time and money on more elaborate developments and designs. But there is no question that thousands of entrepreneurs, start-ups and resourceful individuals benefit from available (often free) web design tools that enable non-techies to "DIY" their websites. You probably heard of Squarespace, Wix or Weebly.
Making a website using free website builders - the "DIY"-way
If you’re on a budget, have lots of spare time, and you're determined enough, there is no reason why you shouldn't try to bootstrap your online portfolio! The disadvantage, however, is that there is a lot of technical, functional and visual limitations imposed by online web builders. So, websites built with those tools are also almost impossible to expand beyond their generic purpose and are often locked to the system they've been designed with - so forget about easy migration and scale! Moreover (and assuming you don't know CSS), your website won't be bespoke, and you will likely cringe while stumbling upon an identical one (your competitor's!). Therefore, your expectations towards DIY website builders shouldn't be to create professional business website that really stands out and takes you to the next level, which is...
Web design for professional businesses
If you’re a small or medium business owner that cares about how the website presents the company brand, and how good it is in actually making money (i.e. conversions) you’re probably better off hiring a professional web designer.
We get to live in the lucky times where a good web designer has a solid understanding of coding, so you no longer need to choose between functionality and the looks. It's also often the case that an experienced web designer will have a good understanding of graphic design. So is undoubtedly qualified to pull off a bespoke, professional business website that will lift you above the rest of the "DIY-crowd" and your competitors.
If you're treating your website as an active advertisement or a real business asset that can draw the attention of your customers - and you should! - then having it done by a professional web designer is without question the best way to go.
High-level functionality in web design
If you need your website to do more than the above, you probably will have to consider investing your money in a developer, especially if you’re thinking about managing large databases of information through your website. If you have a bunch of money on a large team of web developers, front-end designers, artists, project managers, etc. and have plenty of time for everyone to team-up then you can deliver a great professional business website project that will look stylish and modern. If all goes well, it will also be more reliable and capable of handling more complicated tasks like bespoke e-commerce shopping carts and payment processing systems. In a sense, a well thought-out and properly executed high-level website/IT project is infinitely scalable and can handle billions of active users like this website or this one.
However, expect a bill to the floor and, as unfortunate as it sounds, a high risk of failure. As it often is with large, overbudget IT projects.
Who should I higher to design my website?
It really depends on your goals. There will always be some work for developers who get higher paychecks and can pull magical websites that do more than looking good. Some people don’t need to spend a fortune on online advertising or marketing if they can stitch up a basic site from a template for free. However, the sweet spot has never been as available as it is now and you can have a professional, beautiful and functional website with a reasonable price tag and realistic ROI for your business at the same time.