ADC anti-aliasing filter
You need to make sure that noise from aliasing is low enough one way or another.

You mention the signal being 1 kHz square wave, but then say you are only interested in "static DC voltage".  Those together make no sense.  I'll assume you want to measure the top and bottom levels of this square wave.

The first thing to do is decide how fast you can sample.  Aliasing problems reduce with higher sample rate.  You say the A/D can do 250 kHz sample rate, but you haven't said if the system it is connected to can do that.  In any case, that is way more than you need.

Try two poles of ordinary R,C filtering at maybe 10 kHz or so.  If you sample at 250 kHz, then the only signals above 125 kHz will cause aliasing.  Those will be attenuated by about 12.52 = 156.

Only you can answer how much frequency content there will be above 125 kHz, and whether attenuating that by 156 (44 dB) is good enough.  From your description, I'm guessing it is.  If you're not sure, throw another pole at 10 kHz or so at it.

In general, you want to do only enough filtering in analog to reduce aliasing noise to acceptable levels.  If you want to find some "average" or whatever, do that digitally after sampling.  Digital filters don't suffer from inaccuracies due to part variations, temperature, or non-linear behavior of parts.

For the digital filter, you have to decide what settling time you want.  Filter the sample stream so that a step still settles to within your maximum allowed time to within your maximum allowed error.