You have to choose your domain name first. It may be a free service or a paid one, you have to be more firm towards your domain.
In general you should select the domain based on your content and core of your website. For example if your site is about pencil then your domain should also reflect it. You can use tools like Google keyword tool and WordTracker to decide how much your keyword is popular.
Don’t decide your domain name in a hurry. Take your own time and decide based on the content of your website.
Once you have decided your domain name you have to check the availability and register there. To know more about that CLICK HERE
