You can do this in the terminal. It's quick but the command below is probably not the most efficient way and won't work if the filenames have any spaces in them. You can remove or replace spaces in the Finder with the Rename... command.
Let's say your 1,000 images named image0001.jpg...image1000.jpg are in a folder named allPics/. Make another folder next to it called something like selectedPics/.
Open Terminal.app. Type cd<space> and then drag the allPics folder into the Terminal window and hit return. (Type a space, don't actually type '<space>').
Then copy and paste this command and press return :
cp $(ls | awk '{nr++; if (nr % 4 == 0) print $0}') ../selectedPics
This will copy every 4th file from allPics into selectedPics.