Hypothetical situation; JJ Abrams' ST trilogy has ended. The plan is to go ahead with the new timeline, but only a few cast members agree to return. You're in charge, what do you do?
I know the natural urge would be to jump straight to TNG, but this timeline is still young and it needs to be fleshed out more. TNG is almost a century away from present ALT-timeline events, so you have years and years worth of stories to tell. Also, as events have been irreparably changed in this timeline, who's to say TNG or the other series even happen?
Personally, I would like to see drastic changes to make this timeline as different as possible to its prime counterpart. I'd likely kill off most of the main crew (the actors that didn't want to return), introduce several new main characters and go from there. Have new enemies, explore new areas in the galaxy and so on. Likely in the form of a TV series.