You should normally pick a domain name that closely resembles your company name. Short and easy to remember domains are preferable, eg use your company initials, or abrieviated alias. Leave the "Ltd" part off. If you are mainly selling to a domestic market, use a suffix like .co.nz for New Zealand.

If your target market is specifically foreign, register a .com .net or .biz address.

You can purchase more than 1 address for a website, however, it achieves little in the search engines. Search engine will tend to favour your primary name, and will ignore the others. Having more addresses is really only good for managing common mis spellings, or common aliases for your company name that people may enter directly into their address bar.

It is a good idea not to impinge on someone elses trademark. Use this great NZ government website link to search trademarks, domains and companies office in one single search: http://www.business.govt.nz/onecheck