Measure the outside of the PSU for us. That way we can be sure that a new one will fit correctly. Back in the day Gateway and all the major suppliers used proprietary hardware that was impossible to replace; hopefully your gateway isn't from that era.
What other components are you going to put in the computer?
That PSU that you have chosen is just "meh." Its not really anything special, and it would probably power your system...(pending components...) but then again, its NOT high quality. Never skimp on the power supply, because if they die, they tend to take the whole computer with them. I would suggest this
power supply. It is a FSP 450 watt that is highly recommended on this site.
I need your new computer component specs to really analyze your PSU needs.