A member who has signs up on the site will be assigned the basic 'Authenticated' role, but the role will not be active until it is marked active, or 'unblocked.' This can be done by an admin once their dues have been paid. Using the account activation as the method of flagging members who have paid (though other methods are possible), would enable members to be granted certain limited rights on the site which are not available to the general public, although it is not currently envisaged that they will need to log in to the site. The rights they could have on the site can be added under 'People > Permissions' by granted rights to the Authenticated role.
A member who signs up will currently simply be sent an automated email thanking them for registering. The text of this email can be edited at Configuration >People > Account Settings. The links to edit emails are towards the bottom of the page. The relevant email is the 'Welcome (awaiting approval)' one. (Unless members are to be invited to log in to the site, no reference to 'approval' or 'activation' need be made in the text of the welcome email.)