I am completely for a restart of this. SR was decent, now I think it's time to move on with the silver age interpretation of Superman and focus on the modern.
I would rather not have a complete redoing of the origin story because I think it's unneeded now. A story where the characters are already established and just a continuation of the central character and story theme seems reasonable. It worked with Batman, half of the characters just existed, but people already knew who they were why not experiment with a much known character.
The Story: Superman has been on Earth a number of years now, and is renowned for his protection of the planet and the origin is established many years ago. Lois Lane is the top notch reporter of the Planet, Jimmy is a struggling photographer, Perry is editor etc.
The trouble begins when we see a new addition of Lex Luthor for the first time on the big screen. He's not nuclear realestate agent, or a mad scientitst only. But an intellectual character as part of a new global organization of LexCorp.
LexCorp has been illegally excavating for fragments of meteroites in Antarctica and along the way discovers the resting place of a meteorite carrying alien artifacts left over from a long distant planet. Not, Krypton in case your afraid of Zod. But pieces from Mars.
LexCorp takes these back to study their origin very closely, at the same time Lois Lane gets tip from a source of this finding, she soon starts to investigate by sneaking into LexCorp and confirming these findings.
Of course, about the same time, Luthor is messing around with some of the artifacts and closer examination reveals that the evidence indicates a massive destruction of a vast civilzation. A piece of the evidence actually actives a homing beason transmitting to you guessed it, Braniac. He is in the middle of destroying another planet and sends right for Earth.
In Superman's love life, Lois is losing interest in the Man of Steel, as is the entire world at this point. They are becoming no longer amused with Superman flying around and instead only take advantage of his protection and use if greedily for a narccistic society.
Here's where Braniac comes in, in an opening like Independence Day, Braninac moves in over Earth and introduces himself as an integalactic traveller who only wishes to exchange knowledge. This of course makes a media stir across the planet as everyone is interested in this traveler. Superman and anyone associated becomes bashed by him and he is quickly betrayed.
Brainiac begins exchaning knowledge and giving back so to speak to humanity, he finds the cure for cancer, improves the economy of third world countries, and saves cats from trees basically. The whole world is ammused and in love.
Lex Luthor, wanting to be on top of course signs Braniac as his pester media boy and begins taking advantage of him for any gain possible. Superman becomes outspoken and suspicious of Brainiac's motivations, which gets him bashed harshly by the world stage, and especially by Lex Luthor.
The story is not complete without Brainac offering Superman the history of his homeworld. He comes to realize that Brainaic was adopted by the central council on Krypton in order to govern over the masses, but was destroyed in the end. We also find Mars and countless other worlds have had their data collected and been destroyed because of greed and arrogance of many races.
Superman learns the truth and tries to inform the masses of Earth, but of course is destroyed and mocked even more this time. Lois Lane has even become part of this crowd, but becomes even more interested and investigates further.
She even journies up the Fortress to get the inside scoop of where Brainiac could be coming from. She learns and believes the truth and publishes it in a great article in the Daily Planet. She nearly gets fired for the bad press and her career is totalled.
LexCorp of course allows Brainiac to connect with their global media and the world goes dark, a global blackout that is. People begin to realize Superman was right. Things go hectic and Superman representing morals and responsibility here responds to defeat Brainiac, who begins a process to collapse Earth's core. All ends well for Earth, Brainiac is smashed, and society wakes up from its ways.
Luthor is also accused of harvesting Brainiac, but of course knows how to clear his name everytime. Superman and Lois also become closer as a result where they decide to begin seeing each from then on. Only simple dating.
t: It's great to see some things don't change. 
