Scopes are controlled by Site Settings > Search Settings, here is the list of available options:
hich option would you recommend?
I would definitely go for custom scopes because custom search center (with tabs) gives much better end-user experience. (Custom scopes feature is only available with SharePoint Standard or better)
Search dropdown does not display any scopes
The list of scopes that will be displayed in Scopes drop-down can be configured at Search Settings > Search scopes page. Scopes defined in Search Dropdown group will be displayed in the dropdown show above. In case you are missing that group you will need to recreate it.