What effect does the length of the cage on a rear derailleur have on bike setup/shifting?
The cage length is what determines the rear dérailleur’s total capacity. The total capacity equates to how much slack chain the dérailleur can handle. Sheldon calculates it as
(number of teeth on largest rear sprocket - number of teeth on smallest rear sprocket) + (number of teeth on largest front chaining - number of teeth on smallest front chaining).
On my hybrid I have an 11 - 34 cassette on the back giving a difference of 23, and a 48-38-28 set of chainings on the front giving me a difference of 20. This means I need a rear dérailleur with a cage capable of dealing with a total capacity of 43.
Sheldon's page about dérailleur selection is here: http://www.sheldonbrown.com/derailleur.html
There is also a capacity measurement given with dérailleurs which equates to the largest sprocket size it can cope with in terms of the number of teeth.