I personally started DD with the German line. I saw Destroyer_Kuro using smoke/hydro in a ranked match and thought it was cool~ Having Hydro was helpful while learning cap positioning and general torpedo safety, so it's a good tool for learning.
I have to echo a few others in recommending the British DD line.
They are made to brawl, so it's ok to accidently get into a fight with another DD.
They have Heals at later tiers which helps make them more forgiving.
They have Hydro which assists in torpedo spotting while you learn what it's like to be on the frontline.
They have rapid deploy smokes, so you can typically smoke whenever you are in trouble and need safety. Other lines have longer duration smokes so you aren't quite as safe if you stay mobile.