I would prefer they go even further back using canon....
Richard and Mary Parker have one son, Peter.  They both work for the USG as government agents for SHIELD.  Because they are going on a secret mission, they give guardianship of young Peter to Richard's brother, Ben and his wife, May.  Ben and May get word that Pete's parents have died and have to tell Peter.  As a result Pete becomes introverted dealing with that knowledge.  Immerses himself in science which he excels at.  Then, one day...Peter Parker attends a science exhibition where he is bitten by a genetically altered (previously radiated) spider. Peter later discovers the spider bite  has given him an array of 
spider-like powers,  including wall-crawling, superhuman strength, speed and agility, and an 
extrasensory  "spider-sense".
Peter initially sets out to find fame and fortune, 
winning a match  while wearing a makeshift disguise against 
professional wrestler  Crusher Hogan (not Bonesaw McGraw like Raimi thinks). He attempts to interest a television network in the idea  of featuring him as a costumed hero (with the advantage that he can  actually do the things his character can), and creates the Spider-Man  name, costume, and web-shooters. After quickly becoming a minor  celebrity, Peter appears on a television special, but afterward allows a  thief (Dutch Malone) to escape the TV station, asserting that it isn't his problem. He  comes to regret his inaction when he finds out that the same 
burglar subsequently  killed his Uncle Ben.
Realizing that he could have prevented his uncle's death, the  guilt-ridden Peter commits to a life of 
crimefighting and lifesaving, driven by the  words, "With great power there must also come great 
responsibility".