Are you sure you want to start your first gluten free baking adventures with a bread machine?
If you had all the ingredients and were following the recipes designed for it very closely, it's one thing, but these flour mixes are all going to react completely differently.
Try calling the grocery back up and seeing if they have tapioca starch, which is the same as tapioca flour, and is commonly used in things like pudding. The starch, not the pearls.
Tapioca becomes gummy when mixed with liquid and baked. Don't bake with tapioca all by itself unless you want rubber. Tapioca is typically used as about a 1/3 of mixtures such as
tapioca
rice
corn (starch)
tapioca
rice
potato (starch)
then other flours, which tend to be golden in color, are added in smaller amounts to add texture or taste, such as sorghum, amaranth, bean, quinoa, nutmeals. Garbanzo flour can be used for garafava flour, which is just 2 beans mixed together that nobody can find in the stores anyway. Coconut flour is technically a finely ground nut meal flour with very little starch.
Arrowroot is starchy, like cornstarch, as was mentioned.
What you could do then, is this. As your base flour mixture, use:
1/3 rice
1/3 arrowroot
1/3 potato starch
and then to this, add small amounts of garbanzo and coconut flours mixed together in a half and half mixture, to make another 1/4 to a 1/3 of a cup that would be added. (I don't use soy flour, ick. plus I had to cut back on soy consumption. you may use soy if you want to.) Or you could use flax meal, or ground up nut meals you make yourself, such as almond or walnut or pecan. It's easy to grind nuts in a blender.
So say the recipe called for 2 1/2 cups flour. you'd use:
2/3 cup rice
2/3 cup arrowroot
2/3 cup potato starch
1/4 cup garbanzo
1/4 cup coconut, or ground nuts
But bread machines are really wierd even with regular flour, so I'd try making this as a batter bread first in the regular oven and use smaller than normal bread pans to see what it does and how it comes out and how it tastes first. One thing you can do with oven baking is watch the bread and test it when it's "supposed" to be done by pulling it out, knocking on it, and then sticking a knife thru it to see if the knife comes back out clean and dry or sticky. If the knife is not clean, it goes back in the oven to bake some more.