If you already have the 350w power supply, and it's a good quality unit, and it can provide most of the rated power on the 12v rail, it should be sufficient, assuming that the rest of what you have is a relatively basic system.
I'm running a G3220 (54W TDP) and R7 250E (55W TDP) - rest of system 1x4GB RAM, one HDD, one optical drive one massive CPU fan. My power supply is rated at 220W, and the 12V rail can provide up to 216W (18A on 12V rail). My system is cutting things close, but it's doing the job. If your system is similarly configured, 350W should be plenty.
If you don't already have a Power Supply, though, I'd go with Herc's suggestion.
EDIT: ah, yes, you specified the VS350. That does have 25A on the 12V rail, but, I notice from Corsair's website that it's a 200-240V unit. If you're in the US (or a few other countries), that's a no-go.