You can certainly use that thread for practice, and lots of people would use it for piecing and quilting.
After years of quilting, though, I have found I prefer Aurifil 50wt 2-ply for piecing. It is a finer thread with very little lint, meaning I need to clean the bobbin area less often plus the bobbin holds considerably more thread. I haven't tried Masterpiece or Prescencia, but those are also very high quality threads for piecing.
With thread, the higher the wt the finer the thread. A newer way to measure thread size is Tex; the higher the Tex number, the thicker the thread. Ply is the number of threads twisted around each other. Typical "regular" thread is 50wt 3-ply.
For quilting, it depends a lot on the look you want. I happen to like thin threads for quilting because they aren't so obvious (my mistakes don't show as much!). My current go-to thread for quilting is Glide, which is a very strong 40wt polyester thread that provides a hint of shine. It is available online at
http://www.bobbincentral.com/ . Their
Edit: Where are you looking for thread? The ones I listed are typically available online -- much more difficult to find locally. If you are shopping at JoAnn's, then Mettler and Gutterman regular lines (these would be the spools with the largest selection of colors) are fine. I used to use Mettler silk-finish 60wt thread for piecing (this would be a very good thread for you to start with) until I tried Aurifil.