I just ripped up my 30 year old basement carpet. There was significant efflorescence on the floor along along an exterior wall, where carpet padding wasn't used. The carpet in general felt "sweaty" and the underside had moisture stains in a few spots. Finally, sections of the floor with older concrete looked wetter. There was no trace of standing water, though.
My inclination is to vacuum the efflorescence and let things dry out for a week or so before laying down new padding and carpet with the plan to repeat in 5 years or so. Is there any other prep work I can/should do?