I have successfully quilted with YLI nylon monofilament thread. If you are using a walking foot, the stitching will be safe for children. The safety issue comes in only if you have big "toe catcher" stitches (which are more common in FMQ by beginners, not really an issue with experienced FMQers). It holds up just fine over time. It *can* deteriorate if exposed to a lot of sunlight for long periods of time (years), becoming yellow and brittle; however, with normal use it can easily last 20 years.
Some people prefer polyester monofilament thread, such as Superior sells. This thread does not turn yellow or break down over time, so you might want to use that instead of nylon monofilament. I prefer nylon monofilament for invisible machine applique because it is less noticeable; however, if I were quilting I would probably choose Superior's polyester monofilament thread. Also, polyester monofilament is less stretchy than nylon so it requires fewer adjustments to tension than nylon does.
For nylon monofilament, you want to reduce the upper tension considerably. This is to compensate for the stretch in the thread. It is also important with nylon monofilament to underfill the bobbins; for a metal bobbin, fill only about 3/4ths full. Those are the two major adjustments I make for nylon monofilament. Polyester monofilament is similar, but you would probably need to loosen the upper tension somewhat less.
Whether using nylon or polyester monofilament, brand is important. The only ones I recommend are YLI for nylon and Superior for polyester. Neither of these threads is "pokey". The nylon is as fine as baby hair (which is where the risk comes in for baby quilts if the thread gets wound around a toe or finger). Polyester is just slightly thicker and a little more milky in color, whereas nylon is clear (or smokey).
If you are wary of monofilament, then I would suggest going with Superior's "Bottom Line" in silver. This is a very fine thread, and the silver blends in with everything. Here is a link to it:
http://www.superiorthreads.com/shop/...om+line+silver