If you want your arms to grow, work them out the same day you work legs. With clients, I usually like to work the legs first, because of the amount of energy it takes. But if we have a lot of upper body and core work to do, we will do them last. The elevated hormone levels (which differ from men to women) generated from working legs pay off both during the workout, and during near term recovery. If you hit legs first, you will experience higher hormone levels throughout the workout, which is a boon to any exercise enthusiast. A study was done which divided people into groups: group A, those who trained their arms all by themselves, and those who trained legs and arms during the same workout session, twice a week for 9 weeks. In the group which trained legs and arms together, isometric strength increased by 37% vs. 9% in the control arm. This was due to the subjects in the first group experiencing much higher Plasma Testosterone Plasma Growth Hormone levels.
Hansen, S., T. Kvorning, M. Kjaer, and G. Szogaard. The effect of short-term strength training on human skeletal muscle: The importance of physiologically elevated hormone levels. Scand J Med Sci Sports 11:347-345. 2001