I was going to comment on the case as well, but the more I thought about it, you should be OK. The power supply is underneath the motherboard tray, I think, so cable routing would be alright, especially with it being a fully modular PS. (Only the cables you need will be in there.
I would like a little more head room with the PSU, but the 620 should do just fine.
Take it slow, keep the manuals open and well within reach, and everything should work out well.
Have fun