My greatest concern when I read posts like this is if you have absolutely no idea what you need to build a fixed gear bike then how do you expect to build one that is safe? Fixed geared bikes are indeed simple machines which of course is one of their greatest assets. That said, simplicity can also be a deficit. You see, when something is brought down to the bare minimum then absolutely everything that is left must function properly. Getting it wrong can cost you dearly. Even the folks who know exactly what they are doing are taking a certain risk when they mish-mash a bike together.
Opinion time - If you don't know what parts you need to build a fixed gear bike then one of those parts should most definitely be a front brake at minimum. I'm not taking a cheap shot when I say if you don't even know what parts you need then you are absolutely guaranteed to not have the skills required to effectively (safely) navigate such an advanced machine and you do not want to learn those lessons as you go because the costs are just too high.