Looking for grip wrapping variations and guides

Not that I'm a huge golfer but I'm thinking of the old saying, "drive for show--putt for dough." ;) For anything I'm going to use frequently, you already hit on one: a medical or athletic tape you like; I'm fortunate lately that the Dollar Tree stores near me now stock black athletic tape.

To look a little less "modern" on some I super use though, I also often use a few layers of either burlap or jute cord, as larason said, with glue. (If as usual I'm too cheap/lazy to use hide glue--Titebond III. God I love the stuff.) And to me these surfaces give an ideal amount of slight roughness to grip.

Funny thing is, I even aesthetically love the latter more. The sword-related art I grew up with is stuff like Barry Windsor-Smith's Conan, so "rustic" cord wrapped handles are way preferable to what I own to the prettified high-end pieces. (Same re: scabbards.) Oh, I'll highly enjoy and save a ton of *pictures* of those pieces. :P

But yeah, when it comes to what I own and most use, combining personal aesthetics, ease of application/updating/repair, better functionality, AND much greater affordability? What's not to love about some good old cordage and glue?

The bike tape is pretty much the same as the tennis tape, I hate the spongy feel it has very much, unless there are different ones. I have only seen the sponge and the silicone ones, both don't feel good to me on a sword or knife.
Hockey tape is more or less just thin cotton fabric with glue on one side, but the glue is just getting everywhere over time.
I have found some people use self adhering bandages for knife grips, LeMal, did you mean these?

So there is basically no difference than aesthetics with the different cord wrap styles for you?

Another great option I've used a lot is ... rawhide. Don't even need to stitch it at a seam; have enough to wrap a few times around the handle, then tightly wrap it with cord and let dry. It leaves a cord wrap impression that certainly doesn't go away, and to whatever extent you find it too rough you just sand it down. A cross-cultural "Poor man's samegawa" that works on many kinds of swords quite well.

I've tinkered with multiple handle construction methods over the years, and done so for a variety of different weapon types.

My favorite means of handle construction entails starting with a shaped wooden core (I typically use boxwood, poplar, beech, or ash).

I apply hide glue to the wood core, which is then wrapped in a natural fiber cordage (I often use cotton cooking twine). This is primarily done to reinforce the handle against the physical stresses of compression and impact shock, and secondarily to add a bit more cushioning between one's hand and the hard metal and wood of the hilt.

To build up the desired grip shape, I use hide glue to affix leather lace (and/or other custom cut pieces of leather) to the cotton cord wrapped handle core for the purpose of creating risers and swells.

I then wrap the handle core in a relatively thin weight vegetable-tanned leather (typically sheep, goat, or pig skin). After carefully measuring the necessary dimensions of the leather wrap, skiving the edges, applying dyes/colorants and decorative embellishments, I will use a liberal amount of hide glue to affix the wrap to the handle. After carefully aligning the seems, I will methodically wrap the exterior of the handle in twine to compress the leather wrap while the glue sets and dries. This outer cord wrapping will typically leave a pleasing texture in the dried leather.

Of the different handle/grip crafting methods I've tried over the years, what I described above produces the best results in my opinion. I've used variations of this process on everything from swords, daggers, axes, and polearms.