My first Vega (64LC) wasn't stable at stock with a gold rated 650 watt psu (EVGA G2) or with a bronze rated 850 watt psu (Corsair TX), So I ordered an 850 platinum psu (Corsair HXi), at stock it was now fine but not with any sort of overclock including the built in turbo setting, plus the new platinum psu (Corsair HXi) introduced horrendous coil whine so both went back as I was worried about keeping the Vega past the returns window incase it was faulty. The next Vega wasn't stable with the 650 watt psu but it was fine with a new 860 watt platinum psu (Seasonic Prime). I've had 2 more Vega 64's since then a Nitro LE 3x8 pin and a Red Devil, both worked fine with the 860 watt psu,
To rule out the power draw as a potential issue I'd stick with a minimum of the 750 watts AMD advise for a Vega 64, Obviously as you spend time on the settings you should be able to undervolt it a fair bit which will reduce the power draw but I think it's important to make sure it works fine with the recommended requirements (750 watt psu). If it isn't you may have problems when you eventually try to sell it on.