Geeetech GT2560: Electronic safety and power source
Whether 350 Watt is enough depends on the amount of Ampere can be generated over the 12 V lines. Computer power supplies add up the power of all the voltages! A nameless or cheap 350 Watt PSU may not deliver enough power (in the sense that they may never reach the given power), you should check that out. The high-end PSU's are usually well fabricated and can usually deliver more power (but should not be taken for granted!).


a typical (214x214 mm) heatbed is about 12 V/1.5 Ω = 8 Amperes (about 100 Watt),
a typical hotend is about 40 Watt,
steppers and board could draw another 5 Amperes (about 60 Watt)


This totals to about 200 Watt, which your PSU should be able to generate without a problem.

Those green connectors plug in and out of the board don't they, usually with those small pins, transporting up to 10 Amperes is not recommended, you should look up the ratings of those connectors.