I'd start with the Antec Sonata case with Earthwatts 500W PSU, now on sale for a low $80AR.
http://www.newegg.com/Product/Product.aspx?Item=N82E16811129024
I don't like the gloss black finish, but it is otherwise a great mid-range case, quiet, and one of the few with eSATA on the front.
To that I would add:
E4500 CPU - a good dual core option at a reasonable price - $125
http://www.newegg.com/Product/Product.aspx?Item=N82E16819115031
Gigabyte P35 DS3R mobo - $127 - you could save about $27 by going with the DS3L board but it only has 4 SATA connectors while the DS3R has 8
http://www.newegg.com/Product/Product.aspx?Item=N82E16813128050
OCZ Gold 4GB(2 x 2GB) 240-Pin DDR2 SDRAM DDR2 800 - $89
You could save about $40 if budget constrained by getting only 2x1GB memory- which would provide acceptable performance for their uses - but with prices cheap today I would try go for more memory
http://www.newegg.com/Product/Product.aspx?Item=N82E16820227199
EVGA 512-P2-N757-TR GeForce 8600GT 512MB 128-bit GDDR3 PCI Express x16 - $120AR
http://www.newegg.com/Product/Product.aspx?Item=N82E16814130290
This card should handle the uses you described very well, but a video card upgrade is the place to spend more if budget allows and you want more power. Consider the THG list of cards:
http://www.tomshardware.com/2007/12/03/best_graphics_card/
And if you want to review the performance of the different cards in real applications, the VGA charts:
http://www23.tomshardware.com/graphics_2007.html
To these key components, add Seagate 320 GB HD - $85, DVD Burner - $35, and Vista Home Premium OEM $110.
Total cost: $661 before OS and $771 with OS
You can shave $67 off this if needed as noted above.
If that is still too expensive, then you should consider going with a mobo with integrated graphics, saving the $120 for the video card.
Naturally you will also need monitor, keyboard, mouse, and speakers, which are not normally included in system specs listed on the forum.
This will give you a nice system - and if you chose to upgrade the video card it could be a very powerful system.