Do keep in mind that 7950 to 7770 is a significant downgrade if you're interested in gaming. The 7950 is on the mid-end/high-end border and the 7770 is a budget card.
I would stay away from the power supply. That's one of the older, low-end Rosewills before they got their crap together and started getting supplies made by Super Flower (Capstone, Lightning, Tachyon series). The Sirtec ones are OK (Hive, Bronze, Hercules), but I would not go that low.
Nothing wrong with the case you picked. The Storm Scout I recommended because there was a very good deal at the time. The Phantom 410 is one of the standard case recommendations, so nothing to quibble with there.
I would reconsider the PSU issue. The one I recommended is a SeaSonic, which is very, very dependable, and that's an excellent price right now. If you want a long-term evolution system, you want a power supply that will take care of your components long-term.
Lastly, on the GPU issue, for a rig in which you've said you wish to do gaming, a SSD instead of a better GPU is a mistake on a sub-$700 system. If you're not gaming, sure, but you're giving away lots of performance for what is a convenience issue. I will generally recommend a SSD on $1000+ builds that have enough flexibility to make reasonable compromises elsewhere, but on a budget-plus gaming rig, it's not my cup of tea.