The tastiest way to thicken up a stew is with a brown or blond roux.
Start with equal portions of butter (or oil) an flour. Melt the butter or heat the oil, and add the flour and mix thoroughly. You should end up with something the consistency of toothpaste, or a bit looser than that.
Next, cook for a couple of minutes at a medium heat to get the raw flour taste out.
Now comes the tricky part: deciding how far to cook it, and not to burn it!
Roux can be cooked to several stages of "doneness" that are indicated by the color:
Blond, tan, peanut butter, brick and chocolate all indicate how much the flour has been cooked. The darker the color, the more flavor, but the less thickening power.
Also, the darker your roux, the lower the temperature has to be, and the more you must keep stirring to prevent burning. It takes a lot of practice to make a dark roux, but I don't think you want that, since you intend to use this as a thickener. I think a blond or tan roux would be good enough.
Once you reach the doneness you want, ladle in some of the liquid from your stew and stir out the lumps. When you have enough added in to make the roux liquid, pour it into the stew and stir it throughout to get it completely mixed.
I think you'll be amazed at what this does for a stew!