Sorry no time for links but I bet u can find if u need to.
Also check if there is microcenter close by
Viewsonic or Asus monitor 21.5"
samsung F3 HDD
good name brand PSU like Antec, Silverstone, Corsair 600W
case is personal preference
mouse and keyboard as well
headset creative or logitech
There isn't really any point in water cooling if you're not going to overclock, especially at a relatively low budget. It is expensive and high maintenance and theres not a lot for you to gain from it. You can certainly get something that looks nice though, i'm going to assume that by 'cool' you mean the typical gamer case with the LED's and stuff.
For the PC itself i would get this:
Intel Core i3-2100 - $124.99
Good gaming CPU with hyperthreading, good for rendering etc. too.
2x4GB G.Skill Ripjaws X 1333Mhz - $47.99
8GB is nice for rendering and editing and is more than enough for games.
ASRock H61M/U3S3 - $69.99
Cheap board with everything you need and USB 3.0/SATA 3
Samsung Spinpoint F3 1TB - $59.99
Fast and cheap drive with plenty of space.
MSI Twin Frozr II/OC GTX 560Ti - $244.99
Plenty of power for any current games even on a big 1080P monitor.
Coolermaster Storm Scout - $79.99
Plenty of cooling and space, looks pretty cool too and should be relatively quiet.
Antec NEO ECO 520C 520W - $54.99
Plenty of reliable power with all the right connectors.
Samsung DVD Burner - $18.99
For installing OS etc. and this one has free shipping.
Total: $702.92 for the PC tower.
If you want you could then add a SSD, this would make boot times, load times and install times a lot faster. I dont think it is worth it at this budget but this is what i would recommend if you want one.
Crucial M4 64GB - $134.49
Here is a nice monitor too
HANNS-G 21.5'' 5ms monitor (1920x1080) - $129.99
After buying the PC, monitor and OS you should have around $60 left of the $1000. I would buy a cheap mouse and keyboard for ~$20 and get a cheap set of speakers.
Creative Inspire T3130 2.1 Speakers - $38
For the PC with the monitor, OS, mouse, keyboard and speakers that comes to about $990 before shipping and rebates.