If God was not created, and He is eternal, the why was His form - i.e. the Holy Spirit and His Son, perfectly suited to salvation?

The Son only has to exist if Man needed to saved, He is not inherent by any means. Likewise, a similar argument can be made for the Holy Ghost. How, then, can all three Persons of the Trinity be uncreated, inherent in God's nature, yet work out perfectly in order for His plan of grace? I am looking for a trinitarian, Bible-based answer, although Catholic tradition or papal statements may be included as way of explanation.