I plan to buy the R9 380X for my fx6300 first of all i would highly recommend to get a good psu EVGA has a line of gold psu from 550w to welders (1600w) all are made using quality components and come with good warranty my friend has the 1600w psu and he got a 10year warranty for it (Not sure how but he did....) As to the psu i feel like you will be fine with normal usage but i would not run stress tests or OC the gpu just in case the psu decided to shit itself its a really good investment to buy a good psu they cost anywhere from 70$-150$ and you will be safe from any kind of bullshit i would not risk the R9 380 on your psu but it should work fine if you wish to do it.
EDIT = A COUPLE EVGA G2 GOLD PSU UNITS DO COME WITH 10 YEAR...