I wouldn't call New World a continuation. Aside from the basic premise and some minor connections to the original it is very much it's own show with original characters. Aside from a pretty camp cameo from one of the original characters in the pilot episode there is really only one storyline so far that heavily connects the two series. All you really need to know is that the ARC is the base of operations in the original series. And now you know, so when you see something that says "ARC" on it and the characters don't know what it means, you will.
It's really up to you. If you would rather watch NW first then go for it and if you like it I'm sure you'll watch the old series anyway and will have some cool "Oh, I get it now" moments.
Although, I was high when I watched this.
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