What language is nearest in structure and vocabulary to German, thus easiest to learn?
Hm, I don't think it would - there are major differences in grammar, while a person from Hamburg and a person from Munich use the same, e.g. for future tense: Dutch "ik zal" (which you could read as "ich soll"), German "ich werde" (or variations of it in dialect, like "ik werd", "i wer"...)
Dutch. I started to learn it on Duolingo some weeks ago. It is very similar to German. There are differences of course, in particular regarding spelling and pronounciation but they are not too difficult to remember.
It is no coincidence that many Dutch people speak German fluently. Also vice versa, if a Dutch person talks slowly a German person (without knowing Dutch) would be able to understand at least some part of what has been said .