Should I use the stock cooler and fan that comes with the Fx 8350 or should I get something better?

Unless that stock cooler is new, Wraith cooler you'll be annoyed by noise as soon as it worms up. Better pick a more powerful cooler even if you don't plan on OC, your ears would thank you.
So, a cooler with at least 4 - 6 heat pipes and minimum 120mm fan is practically a must if you are going to keep it under full load for prolonged time.