I recently bought a laptop with an A8 3500m and can tell you that it could get you by if you really wanted to play bf3 with everything on low and reduced resolution. So that pretty much eliminates integrated graphics for a good gaming experience in BF3. IMO for a playable gaming experience (smooth FPS with settings still low) you would want an i3 and 540 gt graphics card as a bare minimum...preferable an i5 with 6-8gb ram and the more graphics card power the better. This would be about as cheap as you will be able to get and have decent playablity in BF3 IMO.
Acer Aspire 4755G-6849 w/ Core i5-2430M, 6GB, 640GB, DVD+/-RW, 14in LED HD, GeForce GT 540M, Win 7 Home Premium 64-bit at Memory Express
EDIT...by then amd next gen APU will be out (which should do better than my A8) and new graphics cards and cpu may be out from intel/amd/nvidia. Have to wait and see on that stuff.