First, here are some excellent basic instructions on how to make a roux, from Jack Guidry at Cooking Louisiana, including a photographic color chart. I was going to do similar, but he’s got it covered!
When I first went gluten-free, I wasn’t sure what kind of flour would work well for a roux–bit of a problem when you really enjoy Cajun and Creole food!🙂 So, I experimented. To cut a long story short: the best I have found is chickpea flour (gram flour/besan).
The taste is warm and slightly nutty, and the texture of the finished sauce isn’t weird and grainy like I’ve gotten with browned rice flour. I actually prefer the taste to what you get with wheat flour. (But, I never really liked the distinctive flavor of wheat.) And it seems less prone to trying to stick to the bottom of the pan, even though I generally use 1.5 parts of flour to oil by volume. For oil, I prefer to use fairly neutral ones like sunflower or peanut; butter will scorch in a bitter way if you try to make anything but a really light-colored roux with it, and an olive oil roux makes things taste odd to me (as much as I like olive oil).
Another useful thing is to make at least double what you’ll need for the recipe, and save the rest in a jar in the refrigerator. Especially handy, since I don’t know of any commercial GF shortcut roux in a jar.🙂 It should keep for months in the refrigerator, but doesn’t tend to last that long around here!