ok the ram is defiantly the bottleneck. last time i checked flash animations are not video card intensive, and Wolrd of Warcraft and the like arent known for killing a 7800.
My advice go with an Intel Core2 cpu
this 6300 is a good one to go with.
Are you going with Windows XP or Vista? either way you need at least 1 gigabyte of DDR2 memory, and probably more.
here is 2 gigs of Corsair Value ram, since you wont be playing any high end video games, you can get by with standard ram. but the 2 gigs will make sure you wont get slow downs at all
as for hard drive space 250gigs is a good place to start, any more and you are getting expensive, any less and you might not have enough space.
I use this drive in my own rig, and it is a great drive, i highly recommend it.
As for a motherboard you want one that can support all the newer technologies, like SATA2 and PciX, you dont need to know what all of that means right now, but its good.
this one has good reviews, and it has all of the nifty technologies and hookups you could need
The power supply needs to be at least 400 watts to provide all of the juice you need and still not have any overhead
this one is a solid performer from what i can tell
Since your arent going to be playing Oblivion or Crysis, you dont need the world's fastest video card, that good cause it will really save some cash.
This EvGA card has the muscle to handle your games, and is still at a decent price.
You said you dont need a pretty case. I like the way you think, i have a custom machine and i put it in an old Beige tower i had laying around.
this case is fairly conservative, but it still looks good. It has a "tooless" design that will be good for you, and it has a lot of room and good cooling. It is a good choice.
Thats about it. as for keyboard, mouse and monitor those are not nearly as important which brands you get, except maybe the monitor if you watch alot of dvds.
I may not have gotten the best parts listed so if you guys want to tweak this at all go right ahead.
and by the way this all comes out to $742 USD well below your $1000 budget.