Many of these DNA-binding proteins are very strongly positively charged.
I have purified such proteins in the past running the cell lysate over a cation exchange column at pH 7 to pH 8.
At these pH-values, practically only DBA-binding proteins will bind to the resin and you still have to use a rather high salt concentration to get them off again. The proteins coming off are rather pure after just this one step.
These were different, depending of the host organism.
I usually had my cell suspension and used at small-scale a sonicator at large-scale (manufacturing scale) a high-pressure homogenizer.
If I remember correctly, at small-scale - probably the more interesting for you :) - I centrifuged the cells and suspended them in a PBS-like buffer (e.g., 25mM phosphate, pH 7) before sonication.
I did all my work with microbial hosts. In case you use mammalian cells, you may have to adapt the sample matrix.
In my first answer, I wrote that many chromatin-binding proteins are highly positively charges, as they bind to the DNA. But I forgot to mention, you may also have proteins binding to chromatin that are hydrophobic; the parts of the histones not covered by bound DNA is hydrophobic.