umm, i don't think that cpu number is correct. 3rd gen i5 cpus are 3xxx. And there is no i5-2340 in any generation.
But, assuming you have a 3rd gen i5 and don't want to OC, something like this would work: http://www.theitdepot.com/details-Asus+P8H61-M-LX+R2.0+16GB+GB+DDR3+Intel+Motherboard_C13P17115.html
It would take a 3rd gen i5 and any GPU without bottlenecking anything. Unfortunately, you are limited to micro-atx boards at your budget, so the features (number of USB ports, etc) are limited.
ASHISH's selection also works.