That looks like a good starter pattern IMHO. The reason for 2 sizes of needles is that the smaller one is used for the ribbing. Ribbing tends to be looser than stockinette and if you use the same size needles for both your ribbing wont give the same fit. Check your gauge with the larger size and when you are satisfied that your gauge is correct with whatever size needle, use that size for the stockinette part and a smaller size for the ribbing.
This is the last time I'm frogging this project for the last time.