Ebbsfleet is a useless station for your purpose, it is on the edge of London and caters from the "park and ride" market from outer London and adjacent areas. Train connections only into and out of London.
Ashford is a better option, it has connections along the south coast. But, if you are going to Southampton that is SW from London (Ashford is SE) it would be quicker to go via London. If you are planning to stop off on the way, you have lots of nice options: Rye, Lewes, Brighton, Arundel, Chichester, Portsmouth all on the rail line.
Ashford also has very few trains stopping there. Current Eurostar timetable is here: https://content-static.eurostar.com/documents/427437_Timetables%20Core%20destination_Issue%2081_UK%20EN.PDF