You can be a page on someone else's domain. You'll also have some kind of advertising associated with those free pages. Sites like Geocities and Angelfire are web communities like that. HALNet gives us this kind of option as well as do AOL, EV1, and most other providers. If you're really serious and, say, you want to put each family member's glossy eight by ten on your site, you may need more space.
Inexpensive packages abound.
One of these packages will certainly get you enough of a base on the Net and many include registering your site's name. This registration is known as domain name registration. They have search engines for databases of these names and can reference this information quickly. Don't be surprised if your name is already taken and you have to try a modification of some sort. These names are being grabbed up at an incredible pace.