Before you rush out and choose your domain name or name your website, you might want to consider the following points:
1. Your Domain Name Should Be Your Website Name

Naming a site after its domain name is important, for the simple reason that when people think of your website, they'll think of it by name. If your name is also your URL, they'll automatically know where to go.

Imagine if your business (or website) is called "Acme", but somebody else holds that domain name. Instead, you have some obscure domain name called, say, "mybusiness.com". What happens when your customers, recalling that Acme has a product they want, type "www.acme.com"? They'll wind up at your competitor's website. One lost sale.

In the modern world of the Internet, where people automatically turn to the Web for information, it pays to have a domain name that reflects your site or business. There are just lesser things for your customers or visitors to remember. Moreover, you don't seriously think that they'll try to memories an unrelated URL just because you want them to, do you? The only people who'll memories it are you and your competitors who want to compare your prices.

What if you cannot get the domain name of your choice? It really depends on how committed you are to that particular name. If you have an existing brand name that you're known for, you'll probably not want to ditch that name just because you couldn't get the domain name. After all, it took you a lot of time and money to establish that name. If so, you might simply want to try to buy over the domain name from the current owner. Check up the "whois" information for the domain, and contact that person listed to see if they're willing to sell it. You probably should be aware that they are likely to want to charge a higher fee than you'd normally get when buying new domains.

On the other hand, if you're just starting out, you might prefer the cheaper alternative of trying to obtain a domain name first, and then naming your website (or business) after the domain that you've acquired. So if you've acquired, say, the domain name "acme.com", then your website and business might be named "Acme" or "acme.com". I know this seems a bit like putting the cart before the horse, but that's the reality if you don't want to lose out on the Internet.

2. Generic Names Or Brand Name Domains?

I know that a number of people seem to think that your domain name really must be some generic name like "cars.com" if you are selling cars. Witness, for example, how much money those generic names are being sold for. But seriously, if you were looking for a car, you'll probably already have some brands in mind, and you're more like to try out things like generalmotors.com or toyota.com rather than just cars.com.

For that reason, I personally feel that a domain name that matches your brand name is very important. The very name that you use to advertise your product is the name that you will want for your domain, because that is the first thing that people will try in their browser. It is also the easiest thing for them to remember, and whatever that is easily remembered, will be more likely to be tried out than the obscure domain name.

3. Long or Short Domain Names?

Domain names can be of any length up to 67 characters. You don't have to settle for an obscure domain name like avab.com when what you mean is AcmeVideosAndBooks.com.

Having said that, there appears to be some disagreement about whether a long or short domain name is better.

Some argue that shorter domain names are easier to remember, easier to type and far less susceptible to mistakes: for example, "getit.com" is easier to remember and less prone to typos than "connecttomywebsiteandobtainit.com".

Others argue that a longer domain name is usually easier on the human memory - for example, "gaecpws.com" is a sequence of unrelated letters that is difficult to remember and type correctly, whereas if we expand it to its long form, "GetAnEconomicallyPricedWebsite.com", we are more likely to remember the domain name.

Some of these arguments are actually academic. It's increasingly difficult to get short meaningful domain names. I have not checked, but I'm fairly certain that names like "getit.com" and "good.com" have long been sold. If you manage to get a short domain name though, the key is to make sure it's a meaningful combination of characters and not the obscure "gaepw.com" in our contrived example above.

Long domain names that have your site keywords in them also have an advantage in that they fare better in a number of search engines. The latter give preference to keywords that are also found in your domain names.

Which would I go for? I'd go for the shorter name if I can get a meaningful one, but I'm not averse to longer names. However, I would probably avoid extremely long names verging on 67 characters. Aside from the obvious problem that people might not be able to remember such a long name, it would also be a chore typing it and trying to fit it as a title on your web page.

4. Hyphenated Names?

Should you get a hyphenated name? There are a few things to consider here:

a. Disadvantage: It's easy to forget the hyphens when typing a name. Many users are used to typing things like freecpluspluscompilers.com but not free-c-plus-plus-compilers.com. They'll probably leave out the hyphens and wind up at your competitor's site.

b. Disadvantage: When people recommend your site to their friends verbally, having hyphens in your domain name leads to more potential errors than when the name does not contain hyphens. For example, how do you think your visitors will refer to your site if it is named "acme-books-and-videos.com"? They might say, "I visited Acme Book and Videos dot com yesterday. It was fabulous." Their friends, remembering that comment later, might type into their browsers "acmebooksandvideos.com". Oops.

c. Disadvantage: It's a pain in the neck to type. Enough said.

d. Advantage: Search engines can distinguish your keywords better and thus return your site more prominently in search results for those keywords occurring in your domain name.

e. Advantage: The non-hyphenated form may no longer be available. At least this way, you still get the domain name you want.

Personally, I prefer to avoid hyphenated names if I can, but I guess it really depends on your domain name and your situation.

5. Plurals, "The", and "My" Forms of the Domain Name

Very often, if you can't get the domain name you want, the domain name registrar will suggest alternate forms of the name you typed. For example, if you wanted website.com, and it was taken (of course it is), it might suggest forms like:

thewebsite.com
mywebsite.com
websites.com

and the like, if they were not already taken as well. The question is, should you take them?

My personal opinion is that if you take the "the..." and "my..." forms of the domain name, you must always remember to promote your site with the full form of the name. Otherwise, people are likely to forget to affix the necessary "the" or "my". For that reason, I always advertise my sites as "thesitewizard.com" and "thefreecountry.com" in their full domain name forms, rather than just "Free Country" or "Site Wizard" (without the article).

 
6. COM, ORG, NET, etc?

One common question I encounter is from people who can't get the ".com" domain of their choice, but find the ".net", ".org" or other country-specific top level domains (TLDs) available (like .de, .nu, .sg, etc). Should they try for these?

 
The first school of thought goes on the premise that it is better to have a domain name of your choice "myperfectdomain" even if it has a TLD of ".net", ".org" or some other country specific extension, than to wind up choosing an obscure domain name for the simple reason you can't get your first choice. Thus they would settle for domain names like "myperfectdomain.de" or "myperfectdomain.net" or whatever. Against this is the argument that if you get a country specific domain, people might think that your business only caters to that country.

Another school of thought finds that ".net" and ".org" extensions are actually quite acceptable domain names. For some, the ".org" extension actually describes the non-profit nature of their organization. 

Others would settle for the ".com" extension and no less. As grounds for their arguments, they cite the browser algorithms used to locate a website when a user simply types a name like "acme" into the browser. Apparently, the browser searches for a domain name "acme.com" before attempting "acme.net", etc. As such, people who do that will be delivered to your competitor's site if you do not also own the ".com" extension. Indeed, even if people do not rely on their browser to complete their typing, many simply assume a ".com" extension when they type a domain name, so if your business is "Acme", they'll just assume your domain name is "acme.com" rather than "acme.net" or some other such name.

As you can see, there are actually good grounds for accepting any of the above views. My personal footnote to the above arguments is that if you get a domain name with an extension other than ".com", make sure that you promote your business or website with the full domain name. For example, if your domain name is "dogandcatfood.net", make sure that when you advertise your site or business, call it "dogandcatfood.net" not "dogandcatfood". Otherwise people will assume a ".com" extension and travel to the wrong place.  

 I will be glad to help you with this.