The best rope out there to make halter out of is a double braid nylon yacht rope 5/16 or 3/8". It will be medium (not too soft, not too stiff) , doesn't stretch, knots stay put and holds up well over the years. I leave mine hanging on the fence outside 24/7 and some of them are 10+ years old. My favorite brand is New England (sta-set) or Samson. Miami Cordage makes a good product too. I have bought roll ends, seconds, odd lots on ebay. There is a guy in Washington that I have bought a lot from but I can't find his site. There is also someone in Canada that I have bought from as well (think he was in BC). Rope is about 60% of firsts even with shipping. They will not advertise who the rope is by but look at the weave and the tracers and that will tell you who it is. New England has the most distinctive weaves. If you want to make yachtline lead ropes stick with the highest quality you can find (again sta-set is my fav). It has the best life and feel to it.
Polypro does not make good halters because it stretches and becomes very abrasive in the sun. It is also very light and has no feel to it. It is cheap but a handtied halter with quality rope is only going to cost about $5.