If you want one for 3D/animation software you're certainly going to want one with a lot of horsepower. Which you should still be able to get fairly cheap.
4 GIG of RAM strikes me as low for your needs and even for computers in general. I'd probably go to 8. I'd also go for a terrabyte hard-drive. Hard-drives and memory tend to be "fairly" cheap so neither of those should really impact your pricing aims too much.
"Problem" is that.... Well.... Windows 8 kind-of sucks. But it's likely what you'll have to go with so be prepared to go with a new OS/interface.
I'd also probably go with a 4th Generation Intel i7 processor. Again, for your needs you'll want a lot of horsepower.
Such a machine, without a monitor, will probably run close to $800. A little over your desired price-point.