Think of your domain name as the address and hosting as the building behind it. You normally need both, but they do different jobs.
For most small businesses, shared web hosting is the sensible place to start. You do not need a VPS just because it sounds more powerful. A good hosting plan should give your website enough resources, SSL, backups and support without making you administer a server.
WebFlag's rule of thumb
Start with the simplest product that comfortably does the job. You can always move up later.
If you are still unsure what fits, tell us what you are trying to run rather than trying to decode a list of server specifications yourself.