To have your own website you need a few things:
1. Hosting with support of relevant services for the operation of the site – for example, support for PHP, MySQL and so on.. T. There are free and paid (with some conditions) options, and you alone, and to provide appropriate equipment and to install necessary software.
2. Domain (site name). You can register a name (usually paid for a period, for example, year) or to look for the free version – for example subdomain.
3. System for the operation of the website – as you say, you can make pages with a program, especially if you have experience with HTML, for example. Another option is to use-ready system – Joomla !, WordPress … seek information about Content management systems (CMS).
4. Design – page layout, colors, menus and so on.. T. There are templates for most CMS, maybe you can develop into something.
5. Content – text, images, multimedia … watch out for the license of the materials we use, as well as legal restrictions.
At first determine what your budget is (how much you are ready to invest in the venture), what exactly are your skills, how much time you can spare for this task and what exactly is your purpose. I think that what you have written as requirements, YouTube will do the job and there is no sense to do site.