Depends on what I need. If I make low poly rocks or trees I use icospheres. If I do hard surface modeling I almost always use quad spheres. I don’t like UV spheres because they’re a pain to texturemap, but I do use them for some purposes and just get rid of that pinchy central triangle mess and replace it with different topo if need be.
Since that’s a Josh Gambrell video I expect he gets his quad sphere from one of the hard surface add-ons. MACHIN3tools has one (which is free in its basic version on Gumroad).
Since I’m an all-quads fan I’d generally go with a quad sphere (aka round cube), but I’d have to say that the UV Sphere is a strong second choice with a particularly useful default UV map and topology (aside from the poles). Any equirectangular projection texture (HDRIs, most of NASA’s free planet maps, etc) applies to it near-perfectly (except for the poles) with minimal adjustment. I’ve found it a good starting mesh anytime I’d be removing the poles.
You might note a theme in the previous paragraph: the UV Sphere has poling issues, two of them, one on each end. Useful as it can be, if you going with a UV Sphere, you’re likely doing something to deal with the poling – careful camera angle, fiddling with the shading settings, replacing the pole faces – something.
I’d never consider an icosphere since it’s all-tris, but I’m not doing game modeling or any other tri-worthy end-use. Anybody saying “X is best!” usually means for their niche, not 3D modeling (or sculpting) as a whole – a lot depends on your workflow and intended end-use.
Blender comes with several add-ons included but not yet installed – one of them, Extra Objects, has an option to make a RoundCube. But I’d usually apply Subdivision and Cast modifiers to the Default Cube to turn it into a quad sphere.
The default icosphere is already very low poly, the big tris don’t matter for that, and since I am just deforming it, the tris don’t get in the way of that either. It deforms in a low poly way; I feel I have more control about where exactly the planes go so they reflect the light just right – it basically looks good quickly without me having to jump through extra hoops. With a quad sphere I’d make a cube, subdivide it, cast it, shape it roughly, decimate it, shape it more precisely – sure, I can see doing that for a certain look, or if I wanted an all-quad process, but not for the look the icosphere is perfect for.
But if you never make low poly art, whether for mobile games, or for that retro look, then the icosphere is maybe not very useful, and the tris definitely limit what you can do with it. As I said, it depends. I’m still primarily learning rather than creating art or models for a specific purpose, and so I’m trying my hands at all sorts of things.
Above you can see that the head-starter is a quads-hemisphere top merged with a UV-hemisphere bottom, the body-starter is a UV Sphere. When finished . . .
. . . the trigons at the base of the head and top of the body have been deleted, the neck area is all-quads. The trigons at the base of the body have been replaced with a tiny quads-hemisphere patch (the rubber duck’s squeaker detailed on the texture map). The final model has “good” all-quads topology with only minimal N-E poles. Although that’s a simple example, the principles are sound for more complex models.