First, consider whether this is going to be worth the time and energy it will take to do it. If you’re happy and comfortable in your institution’s Learning Management System (ie: Canvas or Brightspace), there are many good arguments for sticking with that and learning how to use it well.
However, as Michelle Pacansky-Brock notes, making your syllabus more accessible and interesting to your students through a course website can be fun and useful. There are many free and easy website builders available these days that don’t require fancy coding skills. Wordpress is probably still our top pick for ease and openness. You can make a website using Jekyll & Github (see this great tutorial by the ProgrammingHistorian). Other commercial platforms include SquareSpace andWix, both more geared towards ecommerce, but very easy to use and can be nice-looking, both come with paid subscription options that will allow you to present something slick design-wise or to remove ads (in the case of Wix). Other free options, like Scalar and Backdrop and Omeka are oriented specifically towards academics, and though they’re often more complicated than you need for a course site, they can be useful for virtual exhibitions of student work or collaborative projects. Another option for making a course website is to store files on Dropbox and use Pancake.io or DropPages to convert them into a static site.
For web hosting, you can talk to your university’s IT service about its web options (some institutions have Wordpress subscriptions, etc.), but if you want to use your own server, try Reclaim Hosting.
Building your own course website from scratch is certainly possible but likely more time consuming than it might be worth, particularly if you don’t have prior coding experience. However, if you want to, Codecademy offers a 4-hour course in HTML, CSS, and Bootstrap. You can also use web frameworks, namely Django or Flask. Both Django and Flask are popular web frameworks based on Python.