I like Connecting Threads - their Essentials line is 50wt/3ply cotton, great for piecing or quilting by machine. Some people say it's too linty for them, but I've never had much trouble with it in that way - or any other way, for that matter.
It's very economical and it comes in a bazillion colors. Wait until it goes on sale and buy it in sets - spend more than $50 and the shipping is free. Normally $2.49/1200 yd spool, $9.99/5000 yd cone
Their Essential Pro line is polyester, 70wt/3ply and has sewn well no matter what I'm using it for. I like it in the bobbin or in the needle.
I love the Superior Threads - King Tut and Bottom Line are my favorites from them. I like Bottom Line for hand applique as well as machine sewing and quilting. They're quite a lot more expensive, though and except for the Bottom Line in applique, I don't notice a whole lot of difference in how they perform or how nice they look in the quilts.
50 & 60 & 70 wt threads are great for piecing, because they don't take up as much space in the seam, but you can use any size you want. Same with quilting - I like the very fine threads for some things and the really heavy ones for others.
Try a few different brands and see which ones you like.