If you want a cheap case with decent cooling, look at some of the raidmax cases. They are pretty quiet. They aren't great, but they are good budget cases. The smilodon is a popular one.
The psu isn't about what wattage it says it is. There are different ways to rate psu's. 450w isn't always 450w. This psu is a good one and should be enough to handle the 4830 or 4850. If you have any thoughts of a second card, you will need a bigger psu though. http://www.newegg.com/Product/Product.aspx?Item=N82E168...
My funds are not limitless, but not limited to a specific set of parts. I got a dual core because I don't need a quad core, and my mobo is am3 compatible although not ddr3. I am a console gamer for the most part although I might play some mmorpg's. It was more based on necessity. The AMD phenoms are nothing compared to Intel I7's or C2Q's right now.
So am I right in assuming that you won't be using this for GPU intensive games? MMO's aren't that hard on the GPU compared to FPS, in which case you can get the cheaper 380w Antec. However if you want this PC to be able to upgrade to something good later on, then you should invest more in the Case and PSU. If you thought that maybe someday you would make this more of a gaming rig someday then I suggest you check out the CM-690 case and get a Corsair 650tx PSU.
this is going to be more of a media center pc - most of my gaming will be on my consoles - i will be recording tv, burning dvds/cds, some multitasking, mp3s, videos, at best mmorpg's because they are completely incompatible with console controllers and things of that nature imo
So its an HTPC basically. I think you would be fine going with the HD 4830 or getting a 4670. To answer the thread prompt: you need very minimal cooling for something like this, the CM Elite 332 that I linked will be fine. The Antec Earthwatts 380w will be fine too.