From what I understand, a nail gun designed for concrete is required to shoot into concrete and since I'm renovating one room at a time, it would mean several trips to the rental company if that’s the case. I'm considering using regular list screws with touch-up paint otherwise, but I've read about others who have done similar with cover caps on the screws.
If the baseboard is already painted, it might be difficult to make it look nice with screws and cover caps. When I did the molding in the basement, I drilled 8mm into the wall and inserted a dowel, which I then nailed into with white trim nails. It requires some measuring, but it worked great. Another option is to glue it.
Adhesive?
Adheres well to clean concrete. Otherwise, it's probably screws and plugs that are needed if it becomes expensive/troublesome with the rental company.