The server where you bought the domain probably offers hosting services but usually at a cost. If you want to do it for free, have your domain redirected to whatever free web service you decide to use for your website. Remember, free sites are limited in the number of pages and can have a lot of ads. On the other hand, hosting your own website as in Method 2 above, or having your site hosted where you bought and keep the domain, allows you to pretty much create as many pages as you want, without any advertising you don't put up for yourself.
Many desirable domain names are already assigned and users must search for other acceptable names, using Web-based search features, or WHOIS and dig operating system tools. Many registrars have implemented domain name suggestion tools which search domain name databases and suggest available alternative domain names related to keywords provided by the user.
You could think of the sites that share your server as your roommates; there's really not that much separating you from them. Sure, you can close the bedroom door, but they can still cause nightmares for you in the kitchen and the bathroom. In web hosting terms, all the sites share a single server's resources, so huge traffic spike on Site A may impact the neighboring sites' performances. It's even possible that another site could take down the shared server altogether, if it crashed hard enough.
Moving to another website consists of transferring the website’s files and databases, configuring your site with the new host, and directing your domain’s DNS to the new host. Once you pick a new site host, they can usually help you out with this process. The cost will depend on the host you’re switching to, but it will probably be anywhere from $150-$400.