If he was smart he'd put up Josh and Sharon and have Chelsia be the replacement. I think he has a deal with James, if he was smart he'd put up James but I don't think that's a possibility.
Look, let's be realistic. This HOH term will describe Adam's future in this house. If he puts up one from the other crew, he is the new leader of Natalie/Shelia/Ryan(and number one target?), if he puts up one of Shelia/Ryan/Natalie, he's the fifth wheel in James/Chelsia/Josh/Sharon.
I'd go for the first option, but I'm sure Adam will probably be swayed over to the other side in an illogical move because he's disgruntled by Shelia. He has to look at the numbers and realize what he needs to do.