About 1M rows of data. Should I restrict myself to few columns as well?

Question

I'm trying to build a predictive model from about 1 million rows of data. My goal is to predict a certain numerical value.

I have the intuition that I should use very few numerical binary columns so I don't get data points that are too separated, a.k.a., the curse of dimensionality. Is this true? Besides, is it the same for numeric columns?