The 7850 would peak a little over 100W of power draw, I believe, on its own...
but in general I feel like a 600W PSU would be better for your build. The 7850 will require a fair amount of power, as well as the i5, and it's better to be pretty well below the peak rating of your PSU--you must understand that a "380W PSU" means that 380W is the very maximum power output, which may not always be attained, especially as the PSU ages, etc.
A high-quality 500-600W PSU should suffice for your build.
Is the Antec 380 enough for this build? Or should I get a 600W ? First time building my own PC.
for THAT build, YES! but you are going to limit yourself down the road it only has 1 pci-E power connector. a quality 500-550w like supersonic977 suggested with 2 pci-E power connectors is plenty for any single graphic card solution for in the future.