The blotches that you describe sound like efflorescence. This is where mineral salts in the concrete leach to the surface creating a white powder-like substance. You can remove efflorescence by scrubbing down the concrete with a ten percent solution of muriatic acid; (one part muriatic acid to nine parts water). CAUTION: Be sure to add the acid to the water and always wear rubber glove, safety glasses, and protective clothing. It's also a must to have plenty of ventilation. After the solution has had an opportunity to work (about fifteen minutes) rinse the area with clean water.
Since you are going to paint the concrete we want to recommend that you take one additional step in the preparation of the surface by power washing it with a high-pressure power washer. This device will deliver enough power will completely remove any surface residue and will allow for the kind of adhesion that is required for floor paint to last.
Once the concrete has totally dried then paint it with a latex floor paint. No separate primer is required. You may need to apply more than one coat depending upon the quality of the paint.