First off, I would have saved his debut for the night after Starrcade. Let Sting get a clean victory over Hogan that supposedly ends the NWO's reign. The next night while Sting is delivering his victory speech, Bret Harts entrance theme hits and he comes to the ring. Bret ends up saying he is the best there is, best there was, etc, and says he wants the strap. Sting (acting as WCW's best interest and savior) says Bret hasn't proved his dues in WCW and won't become a number 1 contender until he does.
Bret vows to prove once and for all that he is the best, and for the next few months he takes on everything WCW has to throw at him. He has matches with Flair, Savage, Hall and Nash, Henning, Benoit, Eddie, Dean, Jericho, etc but during the middle of this me vs WCW angle, Bret Hart turns heel and reforms the Hart Foundation with Jericho and Benoit. For the rest of this angle, they assist Bret in cleaning up the competition until Bret is on a winning streak similar to Goldbergs. The new Hart Foundation could use Canada vs USA heat while also using real workers vs bodybuilder heat. With 6 man tag battles and factions like the Horseman and NWO to take on, this should put Jericho and Benoit over.
Starcade 98. Undefeated in WCW Bret Hart with the Hart Foundation by his side vs undefeated Goldberg.
And while this might sound petty, I think they should have really put a lot more effort into Bret Hart's theme entrance. Everytime I watched Bret come out to some generic theme, it made him feel second rate. And then the street clothes. The booking was a problem, but I think his second rate presentation was just as much of a problem. He never felt like a superstar to me while in WCW.
Instead of trying to recreate his WWF theme, I would have gone for something totally new and epic. Maybe have Bret himself on the track, repeating that he is the best there is.
I think this, plus my above mentioned post would have made Bret's first year a ton more interesting, with classic matches and a huge feud with Goldberg to close out the year. Classic heel vs classic face.