270x will work with the MB and will be a gigantic upgrade over GT610.
500W is recommended for a single 270x, so this should also be enough, but check to be sure. PSU wattage and maker should are usually written somewhere on it.
Check if the PSU has the required additional connectors for 270x (2 x 6 pin PCIE).
Sapphire supplies with the card two molex to 6 pin PCI-E converter cables (like http://www.amazon.com/4-Pin-Molex-Female-Adapter-Length/dp/B007NMSUUA) but if there is a connector already on the PSU - it must be used.
Check the available space in your case as 610 is a small card, but the 270x is 23cm long.