Ok, so you like ATI. That's cool, even though I'm an nVidia guy personally. (Mainly because the only way I'm familiar with ATI is the cheap builds they offer through HP and other companies.)
There are a lot of options for cases, so do you have any preferences that you desire?
For example, do you want a smaller, low profile case? Or perhaps you want a clear side, or aluminum frame, or lots of options for fans. I see you want a quiet computer (who doesn't), and so less fans will probably be better with the right case.
The power supply is an easier matter, because the hardware you chose basically makes the decision for you. The motherboard has a 24-pin connector and an 8-pin cpu connector, and that filters out half the power supplies on the market (this is the most modern configuration). Also, you need at least 1 6-pin cable for your HD 4770 (2 6-pin cables if you want to go Crossfire). Not to mention various 4-pin and sata connectors for various hardware.
As for wattage, you could probably get away with a 450/500w power supply. However the 450w would be running it close (and you won't have enough power to ever Crossfire), so the best thing to do would be to play it safe and get a 600w or 700w.
My suggestion would be to make sure to get a good brand of power supplies, don't screw around with Rosewill and have to worry about blowing up your computer. I suggest an OCZ StealthXstream 700w, which meets all of your conditions.
http://www.newegg.com/Product/Product.aspx?Item=N82E16817341019
However, there is also an Apevia 680w that is much flashier and has a fan speed control, although it probably wont be very noisy to begin with.
http://www.newegg.com/Product/Product.aspx?Item=N82E16817148022
I prefer to use Ultra power supplies because I love them! They haven't once failed on me and I especially love the modular ones, because it saves you the stress of finding a spot in your case for all the extra cables. However, modular power supplies tend to be much more expensive than regular ones. However, if you have the budget, go for it! It will save you many heartaches.
(Actually, the Ultra power supplies are pretty much sold out right now, but there are more modular power supplies)
Xion SuperNova 800w (Bonus - It's also energy efficient!)
http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=4398387&CatId=2496
Now, back to the case.
Thermaltake Soprano - $70
Pros:
-Up to 4 120mm fans (comes with 1, worth about $10)
-Roomy
-Clear side & front door for aesthetics (note the door won't snag if you have it set on carpet)
Cons:
-slits on clear side may impact visibility into case.
-shiny coating might get smudged easily
http://www.newegg.com/Product/Product.aspx?Item=N82E16811133046
NZXT Apollo - $70
Pros:
-2 120mm fans (comes with 2)(I'm not sure if the one in the front is a true 120mm fan, just because it has holes drilled for it doesn't mean a fan will fit between it and the HD cage. So possibly 3 fans.
-Clear side (This one is very clean, unlike the Soprano.)
-front cover for aesthetics and keeping dust out of optical drives (not that it matters all that much)
-Hard drive cage is sideways, making it easier to take them out if need be.
Cons:
-May have bad airflow with reduced intake ports.
-shiny coat may be hard to keep unscratched
http://www.newegg.com/Product/Product.aspx?Item=N82E16811146025
NZXT Hush - $80
Pros:
-Comes with 2 120mm fans
-Has "noise dampening" foam inserted throughout the case.
-Very clean look, non glossed for easier cleaning.
-Front panel doesn't block power/reset buttons (so you can avoid having to open the door hundreds of times when your system crashes haha.)
-Tool-free drive bays (with option to use screws if drives are rattling.)
-Expansion slots use screws (don't ever use tool-less expansion slot crap, they always suck.)
Cons:
-Only 2 fan ports in the whole computer. If heating is ever an issue, you may need an expansion slot fan
http://www.newegg.com/Product/Product.aspx?Item=N82E16811146035
Speaking of expansion slot fans, if you want a nice one (I use them and they are dead quiet):
Also if you want to add a touch of blue to your case, this will light it nicely.
http://www.newegg.com/Product/Product.aspx?Item=N82E16835106104
Apevia X-Telstar - $75
This is an example of a gnarly case that you don't want
Pros:
-3 120mm fan ports, comes with 2 fans
-Side-mount HD bay for easy HD removal
Cons:
-Shitty optical drive and expansion slot connectors. The kind of plastic that shatters if you bend it.
-LCD display for fan speeds and temperature (that don't work with many brands of fans and temperature probes don't always work as intended)
http://www.newegg.com/Product/Product.aspx?Item=N82E16811144209
I'll be honest, it doesn't look so bad from the outside, but building a pc in it must be a real bother.
And there are hundreds more options available, I just tried to point you in the right direction.
Also, check out TigerDirect.com... I love them and they have great shipping policy. their prices also often match Newegg but for some reason lately they've lost a lot of stock and so have less options than before. But give it a looksie.
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