My casting choices:
Captain Picard - Vin Diesel
Where you know him from: The Fast and The Furious, Chronicles of Riddick, the forward from the book "Thirty Years of Adventure: A Celebration of Dungeons & Dragons"
Cmdr William Riker, Exec. Officer - Wil Wheaton
Where you know him from: Recurring characters on The Big Bang Theory, Eureka
Lt. Cmdr Data, Ops, Second Officer - Brenda Song
Where you know her from: The Suite Life of Zack and Cody
Note: In this timeline, Soong is a traditionalist when it comes to his androids, and also a bit of a perv, so he makes them Asian women rather than having them look like him. (Allows for a Spiner cameo as Soong.)
Lt. Cmdr Geordi LaForge, Chief Engineer - Dulé Hill
Where you know him from: Psych, The West Wing
Lt. Cmdr Worf, Security Staff Chief - Isaiah Mustafa
Where you know him from: He's the Old Spice Guy + misc other roles
Note: In this timeline, Worf's adoptive parents lived in a more metropolitan human environment than in TNG. They still taught him Klingon ways, and he is still Klingon, but he was less of an outsider growing up, and is less surly and standoffish.
Lt. Natasha Yar, Tactical Officer and Bridge Security Ops - Jennifer Lawrence
Where you know her from: The Hunger Games, X-Men: First Class, American Hustle, Silver Linings Playbook
Note: Actress selection based partially on her carrying off the role of Sela as a primary film villain, later.
Cmdr Beverly Crusher, CMO - Kate Walsh
Where you know her from: Grey's Anatomy, Private Practice, The Drew Carey Show, others
Civilian Political Officer "Counselor" Deanna Troi - Hannah Simone
Where you know her from: New Girl
Note: This version of Troi is not nice, and is there primarily to ensure that Federation rules and Starfleet protocols are adhered to during the deep space exploration mission - previous captains have made them feel such positions are necessary. Her past relationship with Riker is what will make her inclined to cooperate with the crew in bending some rules.
Chief Petty Officer and Transporter Chief Miles O'Brien - Ronan Keating
Where you know him from: Goddess, The X Factor UK, the 90s pop band Boyzone
Crewman 1st Class Wes Crusher - Nathan Kress
Where you know him from: iCarly
This version of Wesley is still a bit of a prodigy, and has already attended Starfleet core enlistment training and then served at the Utopia Planetia shipyards where the -D was being completed, working on her. When Dr. Crusher was assigned as CMO for the long-term space exploration mission, he transferred to Enterprise under Starfleet rules that permit families to do so for that kind of mission. Picard feels bad about his involvement in Wesley's father's death, and has asked Chief O'Brien to take the young man under his wing. Wes occasionally knows things about new features of the ship that the older crew aren't familiar with yet. And eventually, this character will be mustanged to officer ranks.