The choice of domain name plays a big role in your seo effort. Generally, your domain name should include the main keywords of the subject of your web site. For example if your web site is about web hosting, it's domain name should include 'web-hosting', preferably, at it's beginning such as 'web-hosting-guide' or 'web-hosting-providers'.
Opting to use a sub-domain of your provider's domain can affect your seo effort, and the result is directly related to the provider's seo. It can bring you good results quickly, or it can hamper your seo efforts drastically. Generally, I prefer to not use a provider's sub-domain unless it's for simple testing stuff.
Remember, if your web site becomes poplar one day, your domain name becomes very valuable and you can sell it for thousands if not tens, or hundreds, of thousands. However, if your domain is a sub-domain of your provider's, it's highly unlikely to become very valuable, and it's even more unlikely that you can sell it for anything.
One more seriously very important thing, about using a sub-domain of your provider's, is the fact that free web hosting providers are known to notoriously just pack up and disappear overnight. If you happen to be using a sub-domain of your provider's at that point, your web site will be as good as dead, will disappear with your provider, and you will have very little chance, if any, to recover your hard earned seo work. On the other hand, if you use your own domain, recovery from such a situation involves no more than copying your web site to another provider and adjusting your name server settings, which take no more than a few minutes to do.
If your site is important, take my advice and spend a few pop on buying a domain name for it. You can get one very cheaply; Here are some domain registrars, which I have used in the past and found to be very reliable, as well as good value for money.
If your domain name is made up of more than one word, use a hyphen '-' to separate the words rather than an underscore '_' or missing out the separator character altogether. Fore example 'free-web-hosting' rather than 'free_web_hosting' or 'freewebhosting'. Although, this is the advice of most seo researchers, the difference between using a hyphen and missing out the separator is debatable. In my experience, I found web pages without a separator rank just as high as those using a hyphen, for the same search keywords and the same domain words.
Given a choice, it's far better to buy an existing domain name, or a recently deleted one, than to register a new one. This is because an existing domain name may already have some traffic, and may very well have lots of useful back links. Watch out for domain names that may have been used for spamming etc.
