If you want the data extension to be refreshed on a regular basis, I suggest using a scheduled Automation with a SQL query activity. However if you like to only manually refresh the filtered data, using a filtered data extension created from Email Studio would be the easier way to go.
Another option for regularly updating the data extension is creating an Automation using a filter activity. SQL queries are more flexible however, so if you like to add more logic to your filter in the future this would be the better option.
Furthermore, using data filters isn't considered to be a best practice according to Salesforce:
Note: Data Filters are not considered best practice for using Synchronized Data Extensions. Only use Data Filters when a Data Extension will only be populated once because repeated filtering on the data can cause unexpected errors. Instead, use the SQL query activity listed in this article.
(Source: Create Data Filters using Synchronized Data Extensions in Marketing Cloud)
Filtering for entries that have a certain field populated is possible in both. For a filtered data extension you just add the field to the filter definition and select "is not empty". When using a query activity you need to add a WHERE-clause like this:
AND [YOUR_FIELD_NAME] IS NOT NULL