You can definitely go with a cheaper case. I think the HAF 912 is the recommended case at the $50 range.
The PSU wasn't included in the pcpartpicker price.
Since you need a monitor, your effective budget is $680 which would align closely with Marest's 680 build. I would recommend: http://pcpartpicker.com/p/kKaL.
Your motherboard is micro ATX. Any case that supports micro ATX (which is most ATX Mid Towers) should be fine. Just make sure to check the specifications.
Alternative ram sticks include: Orange Heatsink, Red Heatsink, Blue Heatsink, Black Heatsink. The only difference between the previously listed RAM sticks are the heatspreaders (the colored metal part), since they are the same stick underneath, just pick the one you like. Corsair alternatives for RAM include: Low Profile Black Heatsink, Low Profile Blue Heatsink, Low Profile Black Heatsink, Blue Heatsink, Black Heatsink. Again, these are all the same sticks underneath and have the same stats as the G. Skill sticks listed earlier.
You will also notice that I decided to select a cheaper 660 still from MSI. The one I chose has a lower stock clock 980 vs 1030, however I don't feel its worth the extra $50. Here is a list of 660s you can choose from: http://pcpartpicker.com/parts/video-card/#c=114&sort=a5 . The way select graphics cards is by 1) Stock Clock (aka. Factory Overclock) 2) RAM Size and Speed (should be about the same across the board at this tier) 3) Fan Manufacturer (actually quite important due to noise/temperatures). Recommended fan manufacturers for Nvidia include ASUS (they're kind of expensive though), MSI, Gigabyte and EVGA (they generally only sell enclosed cards, see how the walls of the cards are covered by plastic as compared to the open configuration of the other manufacturers).
The case was changed to a HAF 912 to save $20. The case is one of the few components where its almost entirely the user's choice. Just remember to choose from a set of 'recommended' cases. Marest's build sticky has a list of cases he recommends. Other sites such as www.reddit.com/r/buildapc and overclock.net have a set of recommended cases.
Recommended the Seasonic M12ii because its modular.
Since your budget is tight, I would highly recommend spending the extra 2 weeks to watch components go on sale. For example, the Seasonic PSU is currently $75, but historically, it will go on sale for ~$60 and it has gone down to $50, although recently the prices haven't been so great.
The following parts don't seem to have much price change:
Caviar Blue HDD
Coolermaster HAF 912
The following components are currently on sale:
The following components may go on sale sometime:
Seasonic M12ii 520W
One caveat, the i5-3350P does not have integrated graphics so you will not be able to use it without a graphics card.
EDIT - I was looking at some Newegg sales and here's what I found.
NZXT 20% off their Cases and PSUs with code EMCJNJB224 expires 10/20 http://www.newegg.com/Product/Produc...ECH-_-NZXT-L5A