How does a FIR equiripple filter behave close to DC?
If you want to know the exact DC gain of your filter take the sum of the coefficients. This is true for an equiripple filter as well as any other FIR filter.  There is no such thing as ripple at DC, because "ripple" is a term used to describe a magnitude variation over some range of frequencies.

If what you are looking for is a flat passband then equiripple can fit the bill.  When using the fdatool in Matlab, notice that the equiripple FIR filter allows you to specify a parameter Apass.  This paramter lets you adjust the maximum allowable amplitude of the ripples in the passband as shown below.  By default it is set to 1, which means that you will have a maximum ripple of 1 dB in the passband.



If you are not constrained to FIR filters, then you might want to consider an IIR filter, depending on your needs.  You can usually achieve the desired result with a lower filter order when using IIR.  This means less computation and less delay.