As you may know a domain name is just a name, not a real website. If you are going to create your website: 1- Buy a domain name. To get a domain name, you have to pay an annual fee to a registrar for the right to use that name. 2- Buy a web hosting service to provide your online space and enable you to get your website online at your purchased domain name.
To get further information take a look at: http://www.threehosts.com/build
You need a web hosting service which supports online payments like, Master Card, Visa & PayPal. It is very important that your service be uptime. It means that you can access your account whenever you want to update your web pages, and your visitors can view your website whenever they type your website address. If your hosting service is not uptime it is real hell!
If you want to start your website I recommend purchase your domain and hosting together. In this way it is possible to get your domain for free. Some hosting services offer this gift today.
If you want to run a successful e-commerce you must choose a reliable web hosting service. The security of your business directly depends on the security of your hosting service. (Hacker safe)
Take a look at: http://www.threehosts.com/business
There you can reach the three reputable companies that are leaders in the E-commerce web hosting industry. They fulfill all your requirements to sell online. By using each of them, everything you need for your business website is provided in one eCommerce Hosting Package.
Good Luck!