Give Satisfaction

Jeeves says: "In my younger days, at the outset of my career, sir, I was at one time page-boy in a school for young ladies."

From what I could gather from my research it seems at that time almost all children were in school up to the age of 12.
The page was the lowest position of the lower servant staff. That made him a footman apprentice.
After that followed in rank footman, second footman and first footman (also known as under butler).
Here comes an interesting and rummy thing: footmen were placed in rank according to their height, size and good looks.
So in the TV adaptation a quick career and his young age as a valet would not have been unrealistic at all. ;)
As a valet he now belongs to the upper servant staff.