Bottlenecking question/ PSU help

So I'm building a new rig for Christmas- http://pcpartpicker.com/p/oIhg

It's a very cheap build as it will be a jumping off point for building a pc. I was wondering if using an i3 with the HD 7770 would bottleneck the system (I don't think it will but I'm uncertain.)

I was also wondering if the PSU listed (Coolermaster Elite 420w ATX12v) would be a good choice for this build. I'm trying to keep it to about $600, but I can swing $625. 

Thanks in advance!

if you can id suggest trying to squeeze the fx-6300 into it instead and get a better psu that is 80+ likea antec,corsair or seasonic

IT's probably one or the other for me. I think I'll stick to buying an 80+ corsair or seasonic though, since reading about the fx6300, it's not that huge of an upgrade for the cost, but an 80+ PSU will save my computer from blowing up! :D