For piecing, I fell in love with Aurifil 50wt 2-play. It seems expensive per spool, but it is finer than regular thread so it goes much farther. It is smooth and creates almost no lint. Its fineness helps seam allowance accuracy. Also, the bobbin thread lasts longer because more thread fits on it.
For quilting, it really depends on your machine and the type of look you want. A lot of people like King Tut, which is a heavier cotton thread, but it is pricey. I found that I really like the look of Aurifil 50wt 2-play for quilting on my domestic machine. Just purchased a longarm, though, and because the longarm stitches so much faster Aurifil 50wt 2-ply won't be strong enough; the previous owner said that Aurifil 40wt works in it, though.
Be aware that thread weight numbers go up for finer thread and down for heavier thread. 60wt is a finer thread than 40wt.