GTX 570 is a 219W GPU and with that power hungry GPU, i'd be comfortable using 700W range PSU. Bare minimum i'd use would be 600W range PSU.
That being said, cheapest PSU that i'd be comfortable using with that GPU would cost $67: Seasonic S12II-620,
pcpp:
https://pcpartpicker.com/product/nB3RsY/seasonic-power-supply-s12ii620bronze
Do note that S12II-620 is old PSU platform (released 9 years ago) and if given choice, i'd go with more modern and up to the date PSU, e.g Seasonic Focus or Focus+ series,
pcpp:
https://pcpartpicker.com/products/compare/WrNypg,RzfFf7/
It's hard to suggest S12II-620 at today's date, despite it's good build quality. S12II-620 is only viable when you don't have better/newer PSUs to choose from or if you're a penny pincher.
You can cheap out on every other component inside the PC except PSU. Since PSU powers everything, it is the most important component inside the PC. Also, while the PSU warranty covers the PSU itself and you can RMA the blown PSU, the PSU warranty doesn't cover any other component the PSU fried.
Most people learn the hard way not to cheap out on a PSU when low quality PSU blows and takes part of the system or the whole system with it. Even entire houses have been burned down because of the fire low quality PSU caused when it blowed up.
Like it or not, if you want your PC to work for years to come without any risk of fire and/or damage to your components, you need to hand out some money for good quality PSU. I'm not talking that you need to go with the best PSU money can buy, e.g Seasonic PRIME 650 (80+ Titanium), which costs $150+ (and which also powers my Skylake build, full specs with pics in my sig). Seasonic S12II-620 i linked above costs $67 and is more than enough for your PC, both wattage and build quality wise.
However, if you go with "budget" PSU, please, do record a video when your cheap PSU blows up since i like to see some good fireworks. Just like seen in here,
youtube:
View: https://www.youtube.com/watch?v=f6snWfd1v7M