if i have a shape i can not wrap my head around. i just go in and draw a wireframe over it. starting with the more detailled parts to see how much resolution i would need in the simpler elements. a ring is always easy to upres
"...my low poly topology is atrocious. I've tried redoing it a few times, but I always end up with a similar result." hmm...well to start with there's a whole heap of redundant vertices or edges that are not contributing too the overall object's silhouette/shape. EDIT: So firstly I'd advise desolving those continuous…
They're starting with a geosphere (think a cube subdivided then smoothed to be more spherical) ; you're starting with a regular sphere that's capped with a pole. Hence the difference in geo.
Gotta be really careful when adding edge loops around a consistent smooth curve. Generally it's easiest to start with more geometry and you can terminate those extra edge loops in flat areas where it wont affect smoothing. I'd probably start with 36 or 72 loops around that cylinder.
sometimes with objects that have a lot of curves occurring in more than one dimension, it's a better idea to start with quad stripping than with any primitive at all. start by defining all major curve profiles with quad strips. then start connecting the strips, eventually working towards filling the holes in-between.