There are two basic steps to getting your site online and registering/reserving a domain name is the first.
A domain name makes up the address of your site and can end in .com, .net, .org, .info, .us, .biz, .tv and more.
Once you have registered your name, you will select a web hosting package from Admin-Hosting.com (2nd step). The web host is the guts of any website because this is where you create and publish your pages, build order forms, add functionality and maintain your site.
If being found in the major search engines (Google, Yahoo, etc.) is extremely important to you, I highly recommend you register a name that contains your major keywords instead of your company name.
Think about it. The average surfer searches by subject, not by proper name. So why it may seem cool to have a name like TimothysToolTyme.com, you'll want to choose a name that includes keywords that your target audience would likely use when they search.
So with that in mind, a name like Tool-Tips-for-Beginners.com would be much better than TimothysToolTyme.com. Sure, you can still list your company name on your web pages, but I believe it's more important to make sure the domain name includes your important "search friendly" keywords if you want to receive traffic from all over.
Of course, you can still list your company name on the web site some place, but your domain name will include all the important keywords you'll want to be found with.
Now, as always, there are exceptions...
If you are just creating a website for a local business, getting traffic from all over the web may not be as important to you. This is because your customers will be local and you may want to grow your brand name in a specific area.
If this is the case, it may make more sense to register your company name and create brand awareness locally instead of trying to capitalize on search engine presence.
For example, let's say you have a company called A.B. Steel & Bros. and you help people get rid of debt, but you're based in Paris and can only cater to residents in this area.
Since you are only servicing local clients, you may not care if someone in Spain can find your site in Google since they are not likely to become one of your customers.
In this case, it's not as important to register a name filled with "search optimized" keywords. You may decide to just reserve the company name, ABSteelandbros.com.
NOTE: Keep in mind that the domain name is not the only factor weighed by search engines when deciding your rank.
The content on your web pages and your site's popularity (inbound links from other sites) is very important too. However, it certainly doesn't hurt to make sure your name is optimized for maximum results.
Here are some more tips on choosing the best domain name:
1) Don't register domain names that are too long and have too many syllables if you can help it. Yes, you can register names up to 63 characters long, but that doesn't mean you have to use all 63 characters.
You want your name to be easy to remember. Not everyone will bookmark your page initially so try to think of something that can be easily remembered -- although I realize this may be tricky since a lot of names are taken these days.
2) Use hyphens if your name is more than 3 words long (unless your name includes 3 short words). A name like carbuying.com doesn't really need a hyphen because it's readable the way it is.
However a name like used-car-buying-scams.com looks better than usedcarbuyingscams.com since there are so many words in the name.
3) Protect your name by registering multiple extensions (.net, .org, etc.) This deters people from copying your name. For example, if you own garden-tips-for-us.com you can also register garden-tips-for-us.net and any other extension that's available.
You don't have to build a site on all the domains, but you can reserve the others to keep people (copycats) from registering them.