a few more pointers for charlie d:
- it sounds like all you need is some practice. if you're having problems with lumping and burning, there's no point in bothering with butter and milk or cream.
make up a large batch of roux using just vegetable shortening or even oil and flour, say 1/2 or even 1 cup each of shortening and flour. cook it for a few minutes, let it cool somewhat, then put in tupperware and throw it into the fridge.
now you can practice with both methods: what is in the pan, either roux or liquid is hot, whatever you're adding (again, either roux or liquid) is cold.
have some cold or room temp. water at hand & heat up a couple of tablespoons of roux in a pan until it starts to bubble. whisk in say 1/2 cup or more cold water and keep whisking while it starts to thicken, being sure to contact all of the bottom and sides of your pan. any parts of the pan in which the sauce is not moving will lead to burning and clumping. as the sauce thickens up and starts to get too thick, add more cold water. again, whisk thoroughly and vigorously. after this point, it should be getting to the point where you can add all of the rest of the liquid if you're using a recipe or add more liquid little by little, whisking all the time, until it's the consistency you want.
- the other method is to have some cold roux at hand and your liquid (water for practice) at a low simmer. for a couple of cups water, crumble in a couple of tablespoons of roux and keep whisking until it's not thickening any more. repeat if you need to.
either way, when you start using stock (for veloute) or milk/cream (for bechamel), you'll need to continue cooking for another 5 + minutes until it doesn't taste "floury".
another point not mentioned so far is your heat/ pan relationship. if you're using a very thin pan on top of an electric stove, you'll have to be very careful to stir vigourously and scrape all of the bottom of the pan. electric stoves acheive a low setting simply by being on at less frequent intervals, but when they are
on, they are extremely hot and can scorch a sauce quite quickly. don't hesitate to pull the pan off the heat and whisk for a while. you'll have better results using a very thick-bottomed pan over a low heat. if all you have are thin pans and electric stove, you can purchase a heat pad/deflector or simply use the top or bottom of a large coffee can to place directly on your stove heating element so that your pan doesn't come in direct contact with the heat.
hope this helps