While you could theoretically host the website files on your own computer, this is not really advisable because most home PC’s are simply not powerful enough and residential internet plans are either to slow or unreliable to guarantee a smooth experience for visitors. It would also require that you run your computer 24/7.
You would still need to buy your domain from a registrar and manually assign your home PC’s IP address to it. Please keep in mind that this only works if you have either a static IP from your ISP or sign up for a dynamic DNS service. You would also need good router that allows incoming connections.
If you didn’t understand anything of this, it is safe to say that for you the best approach is to sign up with a reputable hosting provider. Many offer affordable hosting and some even include the domain in their rental prices.