I think the key to translating Genesis 1:2 is not וְר֣וּחַ (we·ruach, "spirit"), but rather מְרַחֶ֖פֶת (me·rachepheth, "moved"). Better understanding the verb will help us better understand the subject.
rachaph (the root) is a rare verb. It occurs just three times in the Old Testament: here, Deuteronomy 32:11:
Like an eagle that stirs up its nest, that flutters (ye·racheph) over its young, spreading out its wings, catching them, bearing them on its pinions, (ESV)
and Jeremiah 23:9:
Concerning the prophets: My heart is broken within me; all my bones shake (rachaphu); I am like a drunken man, like a man overcome by wine, because of the LORD and because of his holy words.
Like the Genesis passage, the meaning of the verb in the Deuteronomy passage is somewhat unclear - it could mean hovering (the most common translation) or brooding. In any case, it is clear that the (English) meaning of rachaph is diverse.
##Ancient translations##
It might be helpful to look at how some ancient translators rendered Genesis 1:2. The Septuagint offers ἐπεφέρετο (epephéreto), a more common verb (epiphérō), but what a rather generic meaning "to bring upon" which lends itself to a variety of English translations. We have, something like
The Spirit of God (explicit in the Greek, definitely not wind) "was brought upon" over the water.
This translation suggests "bore" (as in bore children) for "was brought upon", while this one suggests "was subduing" (lit. was bringing attack upon).
The Targums render the expression as a whole something like "a (wind/spirit) before Yahweh (came to blow/blew) upon the water". As such, they don't really help to translate merachepheth.
Perhaps most interesting is the Peshitta, which offers
spirit/wind ܡܪܚܦܐ upon the water.
Here ܡܪܚܦܐ perhaps means something like brooded.
##Hebrew##
Returning to the Hebrew, The Institute for Biblical & Scientific Studies suggests that the semantic core of rachaph is something like "continuously moving". This makes a lot of sense as it would explain all the diverse translations, or as their reference says:
The meaning of the verb rhp is the same in three places in which it occurs, and it indicates in all cases violent, not gentle motion
I think it makes sense to read a "parental" vibe into the "actively moving" as in Deuteronomy 32:11, The Peshitta, and arguably The Septuagint. So we have something like
and ruach of God was "actively moving, brooding" over/upon the waters.
What does this mean for ruach? Even without the parental connotation, does it make sense to say a "wind" actively moves? Maybe, but a personal agent is much for likely. Indeed, commentary (current and historical) that sees the passage as largely impersonal (e.g. wind), favor an impersonal verb like "swept", "rushing", or "swirled", while largely personal translations (e.g. spirit) favor verbs like "hovering" or "brooding". ("Moved" is somewhere in the middle, I'd say.) If I am correct about the verb, then the noun likewise demands a personal translation.
Thus, I would favor a translation something like
and the spirit of God was acting upon the waters.
Interpretation
Of course the original author of the passage, was not envisioning The Holy Spirit Christians know. So, what did/does the "spirit of God" mean to Jews?
The Jewish Encyclopedia states:
The phrase "spirit of God" merely describes the divine energy
However, I think that greatly oversimplifies the Jewish view. See the same encyclopedia's article on Holy Spirit. Sometimes, the Spirit was equated with the Messiah. Other times it is associated with the "Throne of Glory" from Isiah 6:1 and Daniel 7:9.
Although I can't fully justify it in this post, I would say the overarching view is that the "spirit of God" is seen as an aspect of Yahweh's essence. That is, one of the ways he can chose to interact with our world.
##Conclusion ##
I think "spirit" is the correct translation. If I was asked for a paraphrase to capture the Jewish meaning of the sentence, I would say something like:
And God manifest Himself such that he could actively shape the waters of Earth.
But the true beauty of the Scriptures, in my view, is that God's subsequent revelation reveals a meaning to the text that the original readers did not see. Christians are not wrong for seeing The Holy Spirit in (some) Old Testament passages, such as this one. They have simply discovered a layer of meaning in the text that was not evident from the beginning.
The translation "spirit of God" allows the Christian to see the Holy Spirit in the passage, while still maintaining the original "aspect/manifestation of Yahweh" intent of the text.