I was always told that polyester thread is much stronger than cotton, & if you use it on a cotton quilt, it will eventually tear the fabric. I am certainly no expert here. I've always used cotton thread because I was told it was better; but I think you could use either one.
As far as mercerized, there's a good definition on wikipedia about what it means. Basically, the thread is soaked in chemicals to make the fiber swell which makes it easier to dye & softer. The process was discovered by John Mercer in 1844 & has been improved since then.