I use monofilament a lot and the BIGGEST tip I can give you is make sure you get a polyester monofilament and avoid nylon. Superior Threads sells a good and inexpensive mono-poly on their website and they have low shipping. I have found that the poly is catching on and you might be able to find it in one of the big box stores but you'll have to look at the label.
The next tip is to use a size 10 needle - it's the size I use whenever I use any kind of polyester thread. It's a thinner more delicate thread so you need a smaller needle. Most people have better results with a different thread in the bobbin, I would suggest a polyester that feels and looks like a cotton. It will still be thin and strong like the monopoly, but it will also have a little grip. A slippery shiny polyester might be a little more tricky to work with, but it's doable.
Just a little note, something to think about. I really don't recommend any kind of invisible monofilament threads in a baby quilt. All you need is one little loop to catch on the baby and it could become a very dangerous situation. Because it's such a tricky stretchy slippery thread it's very easy to conceive that a loop could happen, and I just find it unsafe for little ones.
Good luck whatever you choose, and we of course want to see pictures when you're done!