Thread and the quilting done with it, can often be as much of a design element as the piecing and in some cases it is the only design element (wholecloth). I have stated here often that my thread addiction is almost as bad as my fabric addiction. There are so many options available to us and we should take advantage of them. And they all have their advantages for different situations.
I would say that the vast majority of my quilting is done with 40 wt poly. My thread of choice is usually Glide trilobal polyester thread (I love the subtle shine of it) but I do not use it exclusively. Factors that impact what type of thread I am going to use include what type of quilting I am doing (custom with lots of backtracking, a panto E2E, SITD etc), the ultimate use of the quilt (utility, show quilt, wallhanging), and of course, color.
I will often use several different threads on the same quilt. For SITD I prefer a super fine 100wt thread like Wonderfil Invisifil or monofilament, either Superior Monopoly, a polyester or Filtec (The maker of Glide) Essence, a nylon. I will also use 100 wt when I just want texture but don't want the thread to show at all. And then there are all those yummy specialty threads like metallics and holographics. Here is a link to a quilt I did that used a lot of different threads, each one suited to the look I was trying to achieve. https://www.quiltingboard.com/pictures-f5/quan-yin-show-quilt-t297585.html
Variegated threads I will only use in designs that involve no backtracking as it tends to not be very pretty when extensive backtracking is done, the build up is very obvious and the overlay of the variegation changes the look IMHO. Pantos look great in varigated. I have used King Tut mostly when I use variegated but have also used the Glide version which is a much more subtle variegation of color than King Tut. Here are links to two examples. One I did all in Affinity and the other in King Tut.
https://www.quiltingboard.com/pictures-f5/retirement-quilt-coworker-t293700.html
https://www.quiltingboard.com/pictures-f5/super-bright-colorful-kids-quilt-sunglasses-warning-t297993.html
Color is all preference. I will audition threads by pooling several feet of it over the surface of the quilt, trying to get on all the different colors to see what I like best. Yes you will have areas where the thread will show much more than others but I think that is just fine. In fact, most of the time I try to choose something that shows a bit on all the colors so the eye doesn't perceive the quilting as stopping and starting again, I go for a bit of contrast and sometimes a go for a lot of contrast. Here are two examples of quilting with high contrast thread where the quilting became a design element just as much as the piecing.
https://www.quiltingboard.com/pictures-f5/peony-fantasy-asian-panel-quilt-massively-quilted-t302441.html
https://www.quiltingboard.com/pictures-f5/agave-garden-big-reveal-t270708.html
I have found that the two most neutral colors that seem to play nice with everything are goldy beiges and sage greens. A neutral color, combined with a super fine thread will show only texture from a normal viewing distance of a couple of feet and you will only see the actual thread on close inspection.
There is no reason you can't use those cones you have, even if you don't know the weight or fiber content. If the thread is still strong and behave nicely in you machine use it! The best way to know if you like a certain weight, color or type of thread is to experiment and have fun.