WillBaker, most of the suggestions from other uses will mean building the PC yourself, which you said you don't want to do.
Although it is much easier than you think (I would personally recommend it) I will go ahead and assume you still don't want to go down that route. You wont be able to find a prebuild PC (ie Dell, Acer, e.c.) that will run BF3 on ultra in your budget. The only option really is:
Custom PCs, (if you are not considering building it yourself) I think are your only option, and will give you significantly better performance than companies like Dell.
I just went on to pcspecialist.co.uk and configured a PC that will run BF3 on ultra for £840:
intel core i5 3450
Asus P8-Z77-V LX
8GB RAM
Nvidia GTX 570
500GB HDD
DVDRW drive
Corsair (very good quality) 650W power supply
Windows 7 64 bit home premium.
to answer your question regarding how easy is it to install a graphics card: very easy. the only tool you need is a screwdriver, and you simply take off the side panel, slot and screw in the card into the top/main slot and boot it up! (then installing the graphics card software drivers)