As a concrete example of how different house systems can significantly change the interpretation of a natal horoscope, I have written an article for a certain website, All Things Healing, in which I took the natal horoscope of Gheorghe Zamfir, King of the Pan Flute, who himself is an ardent student of astrology, and interpreted it with Whole Sign Houses versus quadrant based Porphyry houses. I provide a link here:
http://www.allthingshealing.com/Astrology/House-Systems-in-Classical-and-Modern-Astrology/5565#.U1HpolcXT1U
In choosing a house system, the most basic choice you can make is between quadrant based versus non quadrant based house systems. The Equal House System that you mentioned is a non-quadrant based system of house division, as is Whole Sign Houses. The others that I mentioned in my previous post - Placidus, Porphyry, Campanus, and Koch - are all quadrant-based. Although the house placements of planets can sometimes differ amongst different quadrant based systems of house division, the greatest and most significant differences are usually between a quadrant based system and a non-quadrant based system.
You also don't have to rigidly adhere to any single system of house division, as each system has its own particular truth and beauty to it, and offers its own unique perspective on how the planetary energies play out in the various areas of your outer life, which are symbolized by the twelve houses. Explore the various systems and see what rings true with you and your life experience. The most obvious and best place to start this exploration process with is with your own natal horoscope, since it is the central holographic imprint for your own life experience.