How can I visualize a gas giant?

If you could make it down to the core, then yes, you would probably be able to experience a "solid surface" (where I put that in quotes for reasons that should be apparent in a moment).

The question really gets to, though, what you consider to be a "solid" and a "surface" in a gas giant. The issue at hand is what the Wikipedia article stated - as you go down through the atmosphere, you encounter denser and denser material. Gas under incredibly high pressure will start to behave like a liquid, and be as dense or denser than a liquid such as water. There would be no definite point at which you could say the stuff above you is clearly "air-like" while the stuff below you is clearly "water-like," it's a gradient.

You would also get crushed long before you made it anywhere near the core, just like it's only fairly recently that we've been able to build submersible vessels that can go to the deepest parts of the ocean on Earth.

Gasses like ethane may become thick like petroleum jelly as you descend due to pressure then to waxy stuff & so on. Hydrogen & helium are lighter and would remain on top. It would depend on the planets' size and composition and assuming no 'rocky' substance.