+1 for 5850. Any 58xx card is good, but 5850s are the best bang for the buck.
For a CPU, I'd just get an AMD Sempron if it will be a dedicated rig for mining. Maybe an AMD Athlon xII if you can afford it.
I recommend Linux over Windows since it's free. And just run it off a cheap USB stick instead of spending $ on a HD. Linux peppermint is a good distro that is pretty newb-friendly if you aren't familiar with linux.
And no closed case! Just makes it harder to cool the GPUs, and costs more $. Just put the rig in a plastic crate or something - many ideas on the forum for cheap open air frames or racks.
In case you are wondering about other parts:
Mobo:
http://www.newegg.com/Product/Product.aspx?Item=N82E16813138362You can actually fit 3 GPUs on this (using pcie extenders), since it has 2 x1 pcie slots. If you can afford it, try going up to a mobo that has two normal pcie slots, and two x1. I like Biostar for mining, since they run GPUs off the x1 pcie slots no problem (with some brands, shorting pins is required).
This mobo is more expensive, but leaves great room for expansion, since it has 5 pcie slots total and thus can accomodate 5 GPUs. Something like this is your best bet if you can afford it. Asrock is also a good brand for mining.
http://www.newegg.com/Product/Product.aspx?Item=N82E16813157339 RAM = something cheap, 2 G is plenty if you run linux.
PSU
http://www.newegg.com/Product/Product.aspx?Item=N82E16817703028^^ I that is the best bang for the buck I know of, though it may be over your budget. It has more power than you need initially, but again leaves room for expansion. You might find a better bang for the buck if you search, but whatever you do, don't skimp on the PSU - mining requires a high quality PSU.
Good luck!