I have no idea which Duden you searched, but "zuerst" is a perfect german adverb and in no way colloquial at all.

But your example shows quite nicely: online translaters are crap... The yandex translation is simply wrong. If you use the more formal way to say something, then it would be:

Zuerst müsseb sie ein gutes Kochbuch auswählen, dann...

It is possible and correct to use the verb "wählen" hier, but a german speaker would rather not use it and stick with "auswählen" in that sentence.

If you address the reader with "Du" or "Sie" depends on context and your chosen style.

Regarding comma or und: that is absolutely up to you and depends on your preference. Both mean exactly the same, it is just a matter of style and surrounding text, if the sentence sounds better with or without the "und".

I have no idea which Duden you searched, but "zuerst" is a perfect german adverb and in no way colloquial at all.

But your example shows quite nicely: online translaters are crap... The yandex translation is simply wrong. If you use the more formal way to say something, then it would be:

Zuerst müssen Sie ein gutes Kochbuch auswählen, dann...

It is possible and correct to use the verb "wählen" hier, but a german speaker would rather not use it and stick with "auswählen" in that sentence.

If you address the reader with "Du" or "Sie" depends on context and your chosen style.

Regarding comma or und: that is absolutely up to you and depends on your preference. Both mean exactly the same, it is just a matter of style and surrounding text, if the sentence sounds better with or without the "und".