But, [i]this is a different Universe's Warp[/i]. So, what does the Warp look like in the Stargate universe?

The Warp is the reflection of psychic energy of the sentient inhabitants of the galaxy, which in this case, are a lot of humans, Goa'uld, and a few other aliens. At the same time, the Ancients ascended to a higher plane of existence. Just before you reach ascension, you gain (essentially) psychic powers. 

My thought is that the Ancients harnessed the Warp to their own ends and imposed order and rules - that is, ascended beings live in the warp. This also fits with the Ori, who gain power with worshippers, and the Warp's general ability to create self-sustaining entities through belief.

I wonder if there's "shadows" of Goa'uld living in the Warp? They do force entire worlds to worship them, after all.

Alternately, maybe the Warp is just a lot... calmer. This is the Warp long before even the Dark Age of Technology, and there are no Eldar nor Orks.