Most of the better Chinese markets have a lot of various forms of pasta that is made from rice.
They usually cook very quickly so don't give them the old 5 or 10 minutes of boiling that wheat pasta takes or you'll end up with mush. Rather tasteless mush at that.
Don't buy "mein" noodles as in "chow mein". Buy the "fen" or "fun" noodles. They are made from rice or mung bean starch.
To thicken gravy's and sauces of any kind, rather than using wheat flour, use corn starch. It's gluten free and basically tasteless and used in almost all Chinese cooking. It's also used in fresh strawberry pie to make the thick sauce that the strawberries are in. Yum.
To thicken gravy or other sauces, first stir the corn starch into a little water and work the lumps out. Then, pour it into the hot sauce and stir. It will thicken it in a matter of a few seconds.