You can use immunoprecipitation followed by the affinity chromatography. I've done it before and got the high purity antibodies (>95%).
To separate IgG and IgM from the serum (from HUMAN or MOUSE serum), firstly use the protein G column, this allows you to isolate IgG from the serum, and then using protein L column (with the remaining serum sample after the protein G column), you can separate IgM.
If you have a FPLC system, you should purchase 2 types of columns (protein G and protein L columns) and following the manufacturer construction.
Below is the link of columns that I've been using. Hope it can help you.