The extension of your domain name is one important consideration. Common would be .com but other extension like .net, .org, etc. are also being used. A .com for your chosen domain name would be better than the other extensions especially for a business website. With a domain for example like http://shoes.net, you may be sharing traffic with http://shoes.com.
It would be for the best if you don't register your domain name with your host. Splitting them up from the start would help you avoid headaches in the future should you reach a decision of parting ways with your web host. Registering your domain name with a reputable company would generally have a charge of between a dollar to ten dollars depending on length of time being signed up for and the extension used.
As much as possible a shorter domain name would be much easier to remember than a long one. It should be easy to spell especially for your customers who should be able to spell it right the first time. Browsers don't like remembering and typing long domain names. There are likely more typing errors, the longer the name.
Also, do not use copyrights and trademarks of other companies on your domain name so do your research to avoid getting involved with legal battles. While others may not ask for damages under such conditions the worse that they would do would be to take back your domain name.
A good domain name is hard to come by. If you have a great idea for a domain name, you could always reserve it in advance. Domain names come cheap these days. Having a good domain name makes it much easier for you to resell in the future should you decide to.
If possible your domain name should be your business name. Having a different domain name and a business name would be difficult to market and difficult for customers who have to take note of two different names.
Protect you domain from hijack by ensuring that your name and contact info is registered as the technical contact of the domain name and in Whois as the owner of the domain name and website.