Webs.com and others have privacy policies. Read them to see what they do with the information and you can decide if you're willing to be with them.
Having a website that's viewable by anyone consists of:
Having a domain name that people can use to find your site.
You need the files stored somewhere that they can be accessed publicly. (Hosting)
You need to link the hosted files and the domain name. (Name servers)
Domains names vary in price depending on the country selling them, the type of domain name you want (.com, .org, .info, .biz) and the company selling them. Shop around. Free domains are available but check the details before deciding to take one on. Bear in mind that free domains often end up with a bad reputation because spammers often use them.
Also to watch out for when buying a domain name is who can administer the domain details (yourself or only the registering company) and if you're locked in to them if you decide you want to take your domain name registration to another company. Do you have to get them to change details or can you do it yourself?
Hosting: Some companies that sell you a domain name will also host your site. There are independent companies that only want your personal details so they can bill you and there are sites that will host for free and only want your personal details for their records. A good site to use if looking for a free site is: http://www.free-webhosts.com/
Possibly your own ISP gives you website hosting. If they do, there are two possibilities for a domain name:
use a sub-domain name supplied by them such as ~yourname.yourISP.com
Use your own domain name and possibly pay the ISP because you use your own.
Your ISP will have details somewhere on their site about the options.
Possibly your ISP will allow you to host the files on your own computer. If you do this, you need to know how to secure your home network to allow people to access the website but not hack your network. This isn't recommended for anyone except those who KNOW they know what they need to. You will probably still need to buy a domain name.
Name servers: The host gives you the name server details you need and you plug them into the correct place with the company who you bought your domain name through. Within a few days, typing in the domain name will bring everyone to your website. If you move the website to a different host, you need to change the name server details with the company you bought the domain name through and in a few days, everyone will be pointed to the new site. Name server details looks something like:
ns1.orgfree.com
ns2.orgfree.com
and usually there are two of them.
If you just want to play around with website stuff and host it on your own computer and have it only accessible within your home network, you can use Apache which you install and configure on the computer that will run the site. Other computers then connect by typing the LAN IP into their web browser.
To create a website, you need to know HTML at the very least, CSS is good to know as well and so is JavaScript (not to be confused with Java) or you can use a website creator such as Dreamweaver (has to be bought) or Komposer or CoffeeCup (free and paid versions).
If you write it up yourself using HTML, etc. you only need a text editor such as Notepad but it can be useful to get something a bit fancier that can handle HTML code. Programs that can handle HTML code will use colours to show you the different parts of the code and can make it much quicker and easier to find any mistakes you make.
Regardless of how you do your coding, you can have pages checked by W3C's validator:
http://validator.w3.org/ - make sure you include the w3 because if you leave it out, you end up at a site of poor reputation.