Nastaʿlīq is not really representative because it's a calligraphy style not used in Arabic.

I would study those but learn kana first, because it's simpler and might give me a) some idea of how to read Japanese and b) practice with the stroke rules and so on of kanji.

Nah, I think learning kana first would be better, because a lot of dictionaries etc only show the reading in kana anyways, and if they romanize it you don't know which romanization system they used, which might be a little confusing.

Would it be helpful to study Chinese characters first, since they are what kanji (and the principles of their composition) are based on?

But it is the standard for written Urdu, I believe.

The reason why I recommend kanji first is because while you're learning them you won't be using kana for anything. When you're learning kanji you only will be learning the meanings; no readings. If you learn kana first, there's a chance you'll forget them by the time you're done with the kanji.
But, I don't think that learning kana first would be detrimental, either, so it's OK to do it that way.

I'm not sure I understand your question. Kanji are Chinese characters. Kanji (JP:漢字) is just what they're called in Japanese. I suppose the term in English specifically refers to those that are used in Japanese but most of them also are used in Chinese.
But that's exactly what I recommend: to learn kanji before you start learning actual Japanese.

I thought Japanese kanji differed from Chinese. Japanese uses characters which aren't found in Chinese and vice versa, and Chinese has simplified characters.

I knew that, which is why I asked if it would be helpful to study Chinese first. The basic principles are the same but not all the characters are. Right?

Hmm, that sounds like a boring way to learn kanji. Only the meanings, and you can't use them at all.

One only has to look at the progress of non-Japanese raised with kanji to see the logic of [this] approach. When Chinese adult students come to the study of Japanese, they already know what the [individual] kanji mean and how to write them. They have only to learn how to read them. The progress they make in comparison with their Western counterparts is usually attributed to their being “Oriental”. In fact, Chinese grammar and pronunciation have about as much to do with Japanese as English does. It is their knowledge of the meaning and writing of the kanji that gives the Chinese the decisive edge. My idea was simply to learn from this common experience and give the kanji an English reading. Having learned to write the kanji in this way — which, I repeat, is the most logical and rational part of the study of Japanese — one is in a much better position to concentrate on the often irrational and unprincipled problem of learning to pronounce them.

Well I'd want to ideally learn both, but that's quite a burden to take on oneself.