I personally don't use anything when I twist. I do however make my twists small and I do twirl each strand about its axis anticlockwise before wrapping them around each other clockwise. This gives me a very firm twist that holds well, but also keeps my hair from tangling even after many washes.
Here is a slow demo of that way of twisting,
here is a demo of how easy it is to undo the twists even after many washes because the hairs in each strand are separated from those into the others.
I am not sure how bad your fuzz is OP but I actually love it when my twists look a bit fuzzy. The image below (sorry those of you tired of seeing it) shows fuzzy braids after a month and 8 washes. I liked how my fuzzy twists looked so much hence the reason I took the photo
I do find baggying freshens my twists and makes them look as good as new. The baggy causes the fuzz to shrink back into the twists and then the Saran wrap presses on them so that no hair is out of place when I take the baggy off.
This was me baggying after styling my hair for the next day's do:
This was the hair the next morning and all I did was add the hair clip: