Hi Pam,
I use the heavier weight perle cotton to tie mine. I went in and checked for the size, and wouldn't you know the labels were of no help telling the sizes. It is the dishcloth weight that I use. I am sure when you go and look at them in the store, you will see the one I am talking about or maybe choose what you think is best for your quilt. I have also used the embrodery thread, it is ok and seperates after washing to a fringy thing.
You didn't mention the crewel yarn or yarn. I have used those too. Often they are the choice for the texture of soft ties and the colors are limitless. (They don't shrink either) I would just go shoopping and look to see what there is at the store and choose what color and material content that you need. Or .... better yet ... make up a small square of your fabric sandwich, tie it with different mediums and wash it. Then you will know for sure how it will come out after washing and how the colors react with your quilt.
Make sure you place the ties about a hands length away. You want it to last, right? I know people that make up a square card and use that to measure the spacing. Oh and to buy the batting that allows for the longest distance between quilting.
Oh... edited to say.... that you can also use cut lengths of 100 % poyester 5mm ribbon, machine tack in the center of it in the same manner that you woud tie a quilt. A different look alltogether. And don't forget you can tie/tack from the back side if you wish not to break up your designs on the front.