You'll probably get a lot of different answers...but I'll throw in my two cents. I took the introductory classes offered when I bought my machine and the instructor said not to use the cheapo Coats & Clark...now one could say that she was trying to push the thread that she sells in her shop, BUT my mother-in-law who sews more than anyone I know told me the same thing.
For piecing and other sewing I have only used Mettler, Gutermann, or Aurifil. I currently LOVE Aurifil. I struggled, though when using Mettler for my free motion quilting class. I haven't done much since with free motion machine quilting but I did buy some Isacord and have made some practice FMQ sandwiches that turned out good.
I took a beginning hand quilting class where they pushed hand quilting thread (Mettler). However, when I was visiting the other "local" (45 min away) shop, I asked if she carried hand quilting thread and she told me I could use regular sewing thread. I have been liking the thicker thread (so it shows up) and have used variegated Sulky 12 wt on the two quilts that I have finished so far. I would use something thinner (probably) if I were really wanting to enter quilts in shows but I'm just learning and I like the changing colors. I do use Thread Heaven to coat my thread when I am hand quilting.
To tell the size of the thread, it's usually printed on the end of the spool. The smaller the number, the thicker the thread.
Hope this helps.