Respectable Cpu and motherboard, will work just fine for you and has some headroom to overclock or replace with an 8-core cpu later. Good price on Ram for 1866mhz. Psu is plenty big and will work just fine for you. Video card is about the best you can hope for with that budget, but it's a very solid performer. I've worked on that case before and I like it, especially at that price point. Included a Cpu cooler, but you can take that out of the build for the time being.
The monitor is mainly a personal choice, but this one will work just fine for you. I'm gaming on a very similar monitor and I love it. It's not the best or highest performing, but it gets the job done and has a good screen size. Included the obligatory optic drive and OS.
:edit: I did include other merchants, but they are all well respected so no worries there. It was necessary to find the best price. You can buy it all from just the two you prefer, but the price will be higher.
Ultra with a couple of settings turned down to High at the very least. For Ultra you'd probably need an Intel Cpu simply because they are so much better for gaming. If you can even up the budget by a hundred dollars I'd probably recommend an Intel h77 chipset motherboard(AsRock h77m for 70 dollars) with an Intel 3470 Cpu for 190. That would definitely give you Ultra settings in BF3. Wouldn't need a cooler then because your overclocking options are about nil, but it's still a nice setup.
The good thing is with the AMD rig, you can overclock though. So probably overclocked you'd be fine at Ultra on all settings at 1080p(which is what the monitor runs at).