This is actually a bit tricky, as there isn’t a definitive answer.
The technologies you’ll pick will greatly depend on the needs of said customers.
If you want to go the freelance route, you can pretty much pick whatever languages and frameworks you wish to use. Then you’ll just need to find projects that use those. If you want to join a web development agency, you’ll have to meet the requirements and tech used by that agency.
@toastedpitabread has given you a pretty clear answer, I’ll just add my two cents.
WordPress gives you a skeleton to build on. The back-end is already there (written in PHP), and connects to a MySQL database. It’s pretty much plug and play, in the sense that if you wanted something up quickly, you could easily add an already designed theme, add some plugins, and be well on your way to a working solution. That’s for the basic part. Now if you wanted to tweak things a little, you’d have to know PHP to come up with your own scripts, or even develop your own plugins. An understanding of MySQL and relational databases is also a nice skill to have. For the front-end, it’s basically HTML, CSS and JavaScript. Those would allow you to come up with your own designs, rather than relying on a theme that was made by someone else, and available to purchase from a marketplace.
Isnt Wordpress easier and quicker?
Definitely quicker than starting from a blank page, yes. As I said, it’s pretty plug and play. That said, as requirements grow, you might have to tweak the solution to meet the clients’ needs. And then you need to know the languages aforementioned.
Because it doesn’t fit all purposes. WordPress is pretty good as a CMS. If you run a blog or a news website, using WP’s CMS would be easier than coming up with your own custom solution. Good examples are The New York Times, or TechCrunch. They both run on WordPress. But then again not everyone can rely on WP, because not everyone has the same needs. It wouldn’t make sense for Netflix to use WP, for example. Different projects have different needs. For blogs and company websites, it can be useful.
Yes, PHP / SQL on the back-end, HTML / CSS / JS on the front-end. You’re free to use any kind of JS framework on the front-end as well. For the back-end, you’re stuck with WordPress’ way of doing things.
Absolutely. Anyone can sign up for Wix and similar solutions to quickly come up with a simple website. Say you run an interior design business, and just need a couple static pages to showcase your work, as well as a contact form for clients to get in touch. Well in a matter of hours you’d be up and running and voilà, no need the require the services of a web dev. That said, not everyone has the patience / will to actually take the time to do this. I’m sure a lot of people do, otherwise Wix would be out of business – but it’s not for everyone. Such solutions will get better in time, and the lower-end of web developers might become “obsolete”. But not just yet. I don’t think Wix websites can even connect to a database. It’s really designed for very simple solutions. And it’s not web development. It’s drag and drop.
You could start learning the fundamentals straight away. HTML, CSS, JavaScript. Learn how to design a simple website, a simple user interface. You can even start right away:
<html>
<head>
<title>Hello World</title>
</head>
<body>
<h1>Hello, World!</h1>
</body>
</html>
- Save it as index.html
- Open the file with your favorite web browser
- You’ve got yourself your very first web page
Some employers might actually specialize in WordPress, and require you to master the ins and outs of the platform. Usually you’ll be required to know more than just how to set up a WP website, because virtually anyone can learn this very quickly. Many bloggers learned how to set theirs up, doesn’t mean that all of them are web developers, it’s just not the case. You’ll need to know the actual languages used.
Then again, and as I opened this post with, there isn’t a definitive answer. It really kind of depends on the sort of web developer that you aspire to be. Do you want to become a WordPress specialist? If yes then go all-in and learn to master the platform, and look for employers that specialize in it.
If you want to be more employable, these days it’s pretty much required to know an actual framework, as @toastedpitabread mentioned. If you want to build stuff with PHP, you will have to learn frameworks such as Laravel, Symfony, Yii, CakePHP, CodeIgniter… these are the most common ones.
But depending on where you live, and if you want to work in this field, it might not be the best path to follow. It really depends. Enterprise software for bigger companies usually runs on stuff like Java, C#, Node.js (those come up a lot). While Ruby is still pretty common among startups. Python is interesting because it’s picking up pace, could be the next Ruby (if it isn’t already?).
But, for now, your goal should solely be to focus on learning how to build the simple stuff, IMO. A simple HTML web page, that you can make pretty with CSS, and interactive with some JavaScript.
It’d be difficult to even claim for just an internship without knowing the basics. That’s the harsh truth, as the requirements have literally gone through the roof.
But really take it step by step. It’s a marathon not a sprint. Learn the basics well and build from there! 
