For priming new drywall in a basement, would you recommend Sherwin Williams primer, or something like Kilz, or for that matter any of the big box store brands (Behr, Valspar, etc)?

My son seems to start with an allergy-like reaction when he goes to bed over the last few weeks. It only seems to be at night in his room - we're having him sleep elsewhere tonight to test the theory. As I was lying awake listening to him cough last night, two things occured to me to make me want to pull some drywall. It's a ten yr old home and his room is on a corner of the upper level. I noticed this last winter (chicago-area) that he had som ice built up in the bottom corner behind a bookcase. This was in the corner of the room where both walls are exterior walls. I didn't really pursue it at the time. My other wonder is that a doctor recommended a steam humidifier in his room for his spring allergies. We ran it at about 60% for a few hours each night for a while this spring. I kind of assumed it would dry that out over the winter though with the sun shining on the siding. We have a sears HEPA air cleaner running in the room, but it's our two months of the year we can have windows open so it's been off more than not. I am going to pull some drywall in that corner, but would anyone have anything I should especially be looking for? It's also the time of year when I have condensation on my car windows in the morning, so I assume it could be getting in the house as well. Thanks