You will need to replace everything, so your best bet would be to head back to the drawing board.
Your current CPU and motherboard are too slow, as is the IGP for any kind of real use. Since you need a new motherboard and CPU, you will need new RAM as well.
For CPU, get an Ivy Bridge instead.
Newegg.com - Intel Core i3-3220 Ivy Bridge 3.3GHz LGA 1155 55W Dual-Core Desktop Processor Intel HD Graphics 2500 BX80637i33220
You will need at the minimum an H77 board which has the best plug and play support for IB CPUs.
Newegg.com - ASRock H77M LGA 1155 Intel H77 HDMI SATA 6Gb/s USB 3.0 Micro ATX Intel Motherboard
To top that, you will need new RAM. Yes, the system will support 8GB of RAM. I suggest 2 1600mhz sticks, as they aren't that expensive.
Newegg.com - CORSAIR 8GB (2 x 4GB) 240-Pin DDR3 SDRAM DDR3 1600 Desktop Memory Model CMV8GX3M2A1600C11
The games add is dated, as that game was released when the 200 series was popular. To give you an idea, Nvidia has the 6 series out as you noticed. The GTX 660ti is about 4x more powerful at least than the GTX260 and Metro 2033 maxed gives even the 660ti a run for its money. In other words, no the GT 610 is not a good choice and is actually barely better than integrated.
All that being said, need a budget. For Metro 2033 you need a very good GPU, and to run it all a new PSU with a minimum wattage of 550w. Make that a good brand like Seasonic, Corsair, or Antec. You will also need a new case to go with it all.
"Resolution is just a number." #Ubisoft Origin/Steam
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