This is an obvious topic. There are many things that can be used to garrotte a girl; a cord, her nylons, her bra, piano wire. I personally favor a cord. Piano wire, if used with any force is going to cut her throat. If I was going to do that I would use a razor. But these are only my preferences.

Clothing; Concealing a girl's breasts as she dies does nothing for me. Others may feel differently.

Other considerations; location, bonds, and sex; before, during, or after.

She must be naked, full breasted. Having her manacled, secured to a table with a cut-out between her legs would make things easier. Thin plastic-coated wire, such as electrical wire arranged with handles at the end is good, as I like to see it cutting into the flesh of the neck. I would repeatedly release and tighten the cord, so she would pass out and recover again and again. I would fuck her continuously, before, during and after...

Thin cord or ribbon, cutting deeply into the neck.

Topless at least, preferably nude and being raped

Hands cuffed or tied behind her back

a tie, usually silk, is the best!

The stocking she's just taken off, before she can start taking off the other, then both legs kicking desperately as her struggles weaken and finally cease.

I prefer a stocking although a necktie is great as well. My preference is to wrap it wround the womans neck twice and have it cross in the front. I like to see it tighten around her neck and watch the expressions on her face as it tightens. Of course she must at least be topless so that I can watch her tits bounce as she struggles. It can go on for quite some time...

I like to wrap a silk stocking around her neck from behind in front of a mirror so she can watch the expressions on her face as the stocking constricts her windpipe.

i love this done to me!

A rope, scarf, stocking (previously removed from her legs), or a leather belt (that I'm wearing). I use it on her when she is tied to the chair, as a part of well planed torture/execution fantasy.
But there are other objects that could be used in that manner, cables, towel, shoe laces, etc. As a part of a random assault fantasy. Things get wild, quick thinking is necessary. I like to improvise as well.
I do have a steel razor-wire but I never use it in fetish play, too dangerous. I just have it cause I'm fascinated with potential brutality of that tool/weapon.

I've no preferences, so long as there is an intense build up, many words spoken, and the garrotting is done slowly!