First major problem I see...why a Xenon instead of i7 920? The Xenon will not OC nearly as well, and you probably have no hope of reaching 4.0 with one.
Cases really are personal preferences, but its hard to beat a HAF 932 for airflow.
For Monitor, you can probably afford a 28", something like this http://www.newegg.com/Product/Product.aspx?Item=N82E168...
if you really want lower resolution, you would be better off shopping for a 32 to 37 inch 720p LCD TV...there are several in that budget range, some that can handle higher resolutions on the PC input or upscale to 1080.
Cooler will depend on the case you end up with, be sure you have clearance for whatever you choose, but check out http://www.frostytech.com/top5heatsinks.cfm ....just be sure whatever you choose has a mounting system for the 1366 platform.
Case is really a personal choice... there are plenty of great options at that price. I like the Antec 1200.
This monitor looks pretty good, you could still afford a larger one though: http://www.newegg.com/Product/Product.aspx?Item=N82E168...
If you were putting any more cash towards the monitor I'd say to look for an IPS panel monitor instead of the TN--better colors and viewing angle--but to get one for under $400 you'd have to sacrifice resolution and size.
As for heatsinks, look here: http://www.frostytech.com/top5heatsinks.cfm
The list is for 775 processors, but all of those heatsinks either have a 1366 mounting bracket or have a variant that does. Some might run a bit more than $70, but that's saved on the other parts here.
There may be better answers to these questions, but I think it's hard to go wrong with what you're spending... good luck
(Oh, and no idea on the 5870 availability, but given current nonexistent stocks I'd say you'd be lucky to get a hold of one.)
Okay, @other posters... Any particular reason the Xeon is a bad choice? It's the same processor as the 920, just a better piece of silicon. Xeons are just higher binned i7s. People who bought it on Newegg seemed to have good results.