Personally I think Venom should remain his core character with Eddie Brock and symbiote story lines. His origin could be slightly altered but I'd keep it 85-90 the same as the original publishing.
I'd keep the aspects of astronauts going into space to fix a space station which has been playing up. The reason being because earlier, some period earlier, it had been hit with a minor meteor shower. One of the small meteors has a goo like substance, which that specific meteor penetrates the space station.
As the astronauts arrive to assess the damage, they see that the exterior has been badly damaged but not significantly enough to not enter. Which they proceed to do. One of the astronauts finds the small meteor and handles it for sample to take back. As he touches it the goo oozes out and attaches to his space suit. In visible distress after not being able to remove the goo, him and the other astronauts quickly go back to their shuttle and begin their decent back to earth.
The goo still attached to the suit, starts reacting and starts to move up the suit puncturing it before attacking the astronauts flesh. The other astronauts send a mayday of help before the ooze backs away from the astronauts flesh and inside the shuttle it takes on a shadowy tar like form... smashing and thrashing around the shuttle breaking and damaging flight instruments. .
As rescue crews and media arrive at the spot where they believe the shuttle will land, they can visibley see that the shuttle is going to crash land in a near by river or lake or bay.
One of the media is a reporter, Eddie Brock. Who among his obsession with Spiderman, can't believe his luck that his one of the first reporters on the scene.. the shuttle crashes. .
now going into point form for the rest,
* Spider man appears and tries to save the astronauts inside. He pulls them free and breaks Eddie Brocks camera, due to Eddie Brock pestering him for months prior. This is the only appearance by spider man.
* Eddie Brock, once everything and everyone leaves the area for the night sees in the water what he believes to be a human like figure floating. He jumps in only to see its an oil like substance which was spilled in the water into a human like shape.. the ooze/oil substance suddenly attaches to Eddie. It doesnt manifest or react only simply stick to him.
* Eddie goes home humiliated. Throws soiled clothes into washing machine and showers then goes to bed. While sleeping the ooze travels across his crib and attacks Eddie. After a struggle his bonds.
* Eddie runs away into the streets unbeknownst that the ooze suit has given him powers as he jumps incredible heights, sticks to walls and flips cars.
* inevitable scene where he is surrounded by thugs and uses his powers.
now I propose Eddie/Venom as he calls himself now. Starts off as a hero doing noble things and helping people. Before the suit starts manipulating him making him an anti hero. Before he goes 180 and ends up a villain by the end of the movie, possibly killing the antagonist (whoever it may be).
Eddie's transformation from hero to villain should be the center piece of the story. Heshould secretly idolize spiderman before despising him. Vowing to destroy him at the end of the movie leading into a sequel or spider man sequel with venom.
There should be a love interest who leave Eddie, him getting fired, losing his apartment all which lead to his darker future.
JJ Jameson should appear and bridge worlds along with spideys short appearance near the start.
end credit scene could feature one of the meteors which actually landed on earth being picked up by a drunken country bumpkin criminal, where a reddish ooze oozes out and starts bonding with him. ... aka carnage hint.