I can imagine a number of ways for the campaign to play out, but for some reason I keep coming back to Chief getting set against the captain of the Infinity in order to protect Cortana, which results in him being set at least slightly at odds with the UNSC. In terms of what will happen overall, I can't help but think that we will once again discover a Flood infestation and have to deal with it in true Spartan fashion, as well as dealing with a resurgent threat from the Brutes and Sangheili (think I spelled that right) dissidents. I can't wait to see how things play out.
One thing I do hope happens but don't expect to see is that Cortana achieves metastability. Personally, I would very much like to meet the AI that Halsey attempted to make effectively immortal by creating for it an eleventh-dimensional matrix through the use of an "acquired" slipspace drive. And yes, that is speculation based on the contents of Dr. Halsey's journal.
You know, this has nothing to do with Spartans.
I think we will end up fighting beside Spartan 4s as the Chief, though I wouldn't really mind facing them in the campaign either. It'll be interesting to see how they and the marines interact with the Chief with the Spartan 2 project under public investigation.