The R9 cards are relatively power hungry.
A R9-390 needs a 6 and a 8 pin power connector.
That will usually be found on 600-650w power supplies.
It is not the wattage that is important, but the 12v amps. A cheap psu will get it's wattage rating not on the 12v lines where it is needed, but elsewhere.
More importantly, a cheap psu will not have the protective circuitry to keep from damaging other parts if it should fail under load.
Really, try to buy a tier 1 or 2 psu.
Usually, a 650w psu does not cost much more than 500w.
If a 500w unit is enough less expensive, then perhaps a similarly performing GTX970 that runs on 500w would be a smarter buy.
Today, the gpu market is in some upheaval with the GTX1070 and RX480 announcements.
It might be a good time to sit on the sidelines, or buy used from panicked sellers.
Here is a chart for the psu requirements for other graphics cards:
http://www.realhardtechx.com/index_archivos/Page362.htm