Quinn: Ron Livingston (older type) or Bret Harrison (young type)
Remy: Cedric (funny type) or Anthony Anderson (bitter/serious/dramatic)
Professor Arturo: Michelle Rodriguez or Navi Rawat OR Paul Giamatti
Wade Wells: Karen Leblanc or Christina Cox OR Malik Yoba (gay love interest)
If Sliders were to be an actual reboot, I'd want an all-new set of characters. There's no reason not to and it just opens the flexibility of the show to go where-ever it wants without having to stay faithful to the source. Personally though, I'd like to see a sequel which picks up years after the show and follows the original professor who was left behind on another Earth in season 2.
He'd have been working on redoing Quinn's experiments for a while with no luck until the Quinn, Wade, and Remy from that Earth finally return home. The professor then embarks on a quest to find his friends (horrible fates unknown to him) and stop the impostor from living his life. He'd probably take an assistant (perhaps a less annoying Conrad Bennish) and a friend or something, but the Sliders from that world would understandably want to stay behind. The whole first season would revolve around searching for his friends, but as we know that they are mostly all dead the most he'll actually find are clues and primarily the season will explore "What if" scenarios like the first season or two of the original Sliders did.
As they progress, Arturo will learn of the Kromaggs (though he will never meet them) and of how they met their end by some sort of virus. He'll find evidence of Wade's death, and will eventually make his way to the planet they were on in the series' finale where they tell him of Remy's last ditch plan and likely death and that the other sliders have already found a way to continue onto other worlds before he got there. The season will end with him unexpectedly finding Remy alive.
Season two will be about getting home again to rebuild what's left.