Honestly, I don't see why you would need to spend so much to play BF3. I've only just now skimmed a review cause BF3 isn't my kind of game, but it seems to be optimized for dual core processors only. An i3 530 and an i7 2600K benched within 1 fps of each other suggesting it's a mainly GPU intensive game.
Tom's benchmark. I've always found Tom's Hardware to be a bit sketchy, but meh. Overclock your E8400 a little bit (something you can't do with 1155 hardware btw outside of the K series, I personally refuse to support Intel by buying these new chips) and upgrade the GPU and go to 4gb of RAM, if anything.
There's no reason you should have to spend more than $150, especially to play one game.
Turn shadows down to low/medium, reflections to low/off, etc. I know it's all personal taste, but frankly I could not care less about things like shadow quality, reflections, or a few extra shrubs when I'm trying to shoot people in the face... I like to have my textures and geometry high in just about everything I play, but there are plenty of unimportant settings that can be lowered significantly that really don't have much of an impact visually, and zero impact on gameplay, but will make a big difference in boosting frame rates, especially for budget hardware.
I play on a 19" 1366x768 TV. It's an LG 19LE5300, an IPS screen (a rarity in monitors this size), with dual HDMI inputs and a headphone jack. I can have my PS3 and my PC hooked up without ever having to switch cables, and at night I can plug in headphones when using the PS3 and not bother anyone around me. I got this thing for $110 on Ebay. I consider the low resolution a plus, one because it doesn't stretch my 720p PS3 games to fill a 1080p+ (or worse, 16:10) screen, and two it allows me to play newer games with budget builds.
Right now I'm running an 1156 i3 and a GTS 250. I've seen recent deals for GTS 250's at under $40 after rebate, that's less than the cost of a new console game. I'm always a generation or two behind as far as hardware goes, but I have 100% of the fun at a fraction of the cost.
Quality Comparison
They go for a cut and dry Ultra - High - Medium - Low, but you would obviously be able to mix and match with custom settings. You've budgeted yourself $700 for an upgrade, ask yourself if the jump from Ultra to Medium here is worth $700. For some people it'll be a yes, for me it's a hell no. Since you play at 1680x1050 you would probably need a slight GPU upgrade, if you ran 1366x768 you could possibly even get high textures/geometry, medium shadows, low foliage with your existing hardware and have a very decent looking game.
Ambient Occlusion
See if you can even spot the difference between these screens at first glance. I had to back out and read the description then take another look to notice the shadow in the corner where the walls meet. They say ambient occlusion can have as high as a 10-15fps penalty.
More on AA and AO
As far as the console versions, they'll definitely be 30fps locked, probably a mix of low/medium settings. I wouldn't bother when your current PC is already a pretty large step up from what they have to offer.