I don't run a rear brake, but have a front brake. If you have plans to run it as either, a rear brake can be beneficial. I've instructed people where I live who are starting to ride fixed gears to have a front and rear brake until you get used to the motions and remember to not try to coast and stress that once used to it, it is their own decision to remove the rear brake.
[MENTION=393034]bmwjoe[/MENTION] , sorry about your son. I think it is awesome that you built that bike up in memoriam.