When you want to start an online business, choosing a good domain name is a serious business. It is because a good domain name and easy to remember is very important as well as including the keyword.
When you plan to register a domain name, basically you start everything from scratch. Google tends to prevent new websites from appearing in its search engine for a few months or even longer. You have to build up your reputation in the web, get other webs to link to your domain and so on (Getting good inbound links is the key to search engine optimization). However, having said that, building a successful website from scratch often gives you great sense of satisfaction. You do not have to worry about the history of the website, anything about the previous owner and the transfer procedures. There are cheaters around, so you have to be careful.
Extension is important
If you choose a dot com (general), dot com dot au (Australia), or co dot uk (United Kingdom), it will depend on the market you are targeting. If your target is in United Kingdom and you have a dot com hosted in US, it will be harder for people from UK to find your web. This is called geo targeting. In this case you need to consider dot co dot uk, to be well ranked in google.co.uk.
One more recommendation for you is, it is better to register a domain name and buy a hosting plan in the same time and in the same company. It will combine the bill and easier to renew.