I think you're cutting it really close. Strictly speaking that build only uses about 170 Watts under full load, but only having 50 watts of headroom is not recommended, especially on such a weak power supply.
Should be fine. I'm running a pentium G2120 and Radeon 7850 on a Silverstone 300 Watt small form factor PSU and that works just fine. Your graphics card is considerably less demanding than mine so 220watts, assuming you buy a good quality PSU, should work fine.