I understand that there are certain words which are considered 'stop words' and that these include 'the'.
If these are to be avoided in metatags etc, is it also the case that they should be avoided in the domain name?
Yes, to the degree in which the keywords have any effect the more common words within a domain name would be ignored. It is, however, important to keep in mind that search engines only place a limited amount of weight on keywords in a domain name. In my opinion the only time where a site keyword within a domain name wins a ranking war is when all other elements are equal between you and near-ranked competitor.