There are so many beautiful different threads on the market that it is a shame to limit yourself to only a few. There are loads of piecing threads that are just fine to use. There are no hard and fast rules, except as pointed out before you must use the right needle and tension adjustments for the thread you are using. I prefer a finer thread for piecing so I have an easier time of lining up points and intersecting pieces. Additionally you can use a different thread in the bobbin then you do in the top (for both piecing and quilting). You should experiment. Go to a big quilt show that has lots of vendors and buy different kinds or go to Superiors site and order a bunch of "try me" spools. They usually have "try me" specials on almost every thread at a discounted price. But you can't choose the color, they will.
For piecing, my usual combo is Aurifil 50 wt 2 ply cotton in the top and Bottom line 60 wt poly in the bobbin.
For machine quilting on my longarm I have used clear monofiliment (both a polyester and a nylon), metallic, holographic, embroidery (40 wt poly usually), cotton, everything from super fine 100wt silk and polyester to super heavy 12 wt cotton with fantastic results. Oh and I have used numerous types of thread on a single quilt.
One time I used a rayon variegated thread in my domestic to quilt a child's quilt. It seemed to work fine. I have since found out that rayon is notoriously weak and often not colorfast. I donated the quilt to charity so I have no idea how it held up. But since learning that I don't use rayon but others have used it with no issues at all. It all depends on the look you are going for and the application.
Here are some variables to consider when choosing the thread for quilting your quilt.
Is the quilt an art quilt, a utility quilt, a fancy show quilt, a table topper that will be removed when the table is in use or placemats and table topper/runner that are meant to take a lot of use, hot dishes, spills and abuse, or maybe it is a wall hanging that will never be washed with lots of embellishments.
How much stress will be on the quilt? A child's drag around quilt that is washed a lot will take a lot more abuse than bed quilt that goes in the guest bedroom and is only used occasionally and washed infrequently.
Do you want the quilting to stand out, play an equal role or just hold things together with very little or no visible texture?
How long do you want the quilt to last? Are you hoping it will last a very long time and maybe be passed down to children or grandchildren or do you not care and when it wears out you will simply make another?
What kind of batting did you use? How far apart can you space the quilting and will the quilt still hold up and look nice if you quilt the minimum amount needed? (That will need a much stronger thread)
Before choosing a thread for quilting you should consider all these variables and then make your selection.