I tried a few times to make gluten-free béchamel, by using cornflour instead of wheat flour because I have some in my cupboard (for thickening sauces, even though it's somewhat considered cheating!). Now, when I did that, the resulting béchamel was decent, but always with a heavy floury taste, as if I had used wheat flour and put way too much of it. I've read this question and the answers recommending alternatives such as xanthan gum. However, I don't have many of those, so I'm wondering: how could I hide the taste of cornstarch my sauce (without reintroducing gluten, of course)? Right now, I'm thinking more nutmeg, but I doubt that'll be enough…
In an answer to another question, someone else was looking for answers on dealing with thickening dairy. If you want to address thickening with corn starch, here are some beginning steps;
- Use the right ratio of corn starch slurry to liquid: 1 tablespoon corn starch thickens 1 cup of liquid
- Use the corn starch in a slurry: although you didn't mention clumps (which slurrying prevents), I mention this as a best practice for many applications - whisk the corn starch in an equal amount of cold water then pour in slowly while stirring the pot
- Heat the corn starch through: you need to heat the liquid until you can no longer taste the starchiness. Unfortunately with a bechamel boiling isn't preferable, but heating it for an extended period of time at a high temp will cook away the starchiness
Although I understand you are looking for a common thickener, be aware of the possibilities as you may have one on hand one day from some other purpose. If the three steps above don't solve your problem, I think that you may be putting in more effort than just buying some more apt thickener. Even so, corn starch should do fine, it sounds like the problem may just be in the completeness of your preparation.
In addition to MFG's excellent answer above, I'll also comment that I find tapioca starch has a very neutral starch flavor, and that substituting it for cornstarch can reduce undesirable flavors.