In housing terms, VPS hosting is like renting your own apartment in a larger building. You're much more isolated than in the roommate situation mentioned above; it's still possible that a neighboring apartment could causes annoyance for you, but far less likely. In web hosting terms, Site A's traffic surge won't have nearly as much impact on Site B or Site C. As you'd expect, VPS hosting costs more than shared hosting. You'll pay roughly $20 to $60 per month.
By definition, a domain name is simply a human readable form of an IP address. In function it is the destination that you type into a web browser in order to visit a website, such a www.google.com. Metaphorically, it is very similar to how you would scroll to a contact in your cell phone rather than manually dialing the person by entering their full phone number; the phone number would be an IP address and the saved contact would be a domain name. Always buy a domain with a reputable domain registrar.
On the topic of dedicated hosting, many web hosting services also offer managed hosting. This type of hosting sees the web host act as your IT department, handling a server's maintenance and upkeep. This hosting option is something that you'd typically find with dedicated servers, so it's a business-centric addition. Naturally, it adds a few bucks to the hosting cost, but nothing that should break the bank if you have the resources for a dedicated server.