a 350 should be good as long as it's +12v side is 18A or better. and it'll hold up against newer games no problem. My neighbor has one and he plays FEAR, Q4, WOW, etc... on med settings with no worries, but he does have a 450W psu with 23A... (just fyi) but you might want to upgrade if it's proprietary.
Dell 4K S2817Q / Logitech Z-680 / Func MS3 Mouse / Corsair K70
NZXT Source 530 / i7-3770K / Corsair H100 / ASRock Z77 Extreme4 / SoundBlaster Recon3d
Samsung 850 PRO 512GB SSD/Seagate 1TB/2TB/WD 2TB
4x4GB Corsair Vengeance 2133 / PNY GTX 980 ti/ Seasonic M12II 850W