I would like to upgrade my PC in order to play CoH2 on max settings.
I have a budget of $350 and I am thinking of i5 3570k 3.4Gz in combo with new motherboard.
You biggest problem is that even the cheapest i5 is pretty well $200. That means that even with a piece of crap mobo ($100), that only leaves you with $50 for memory, and COH 2 essentially screams for at least 8GB, which costs $70. Therefore, you simply can't have an i5 and a new (tolerably decent) motherboard and 8GB of DDR3 ram for your budget of $350. Instead, you should grab an AMD FX-6300 for $120, a decent AM3+ mobo for $95 (like the Asus M5A97 Rev. 2.0), and 8GB ram for $70, or even 16GB (2x8GB DDR3) for $140. Going with the AMD 6 core FX-6300 means instead $120+$95+$70 = $285. With this kind of saving, you could even spring for 16GB ram ($120+95+140 = $355), or $60-$70 for a water cooler for silently overclocking the FX-6300.
Good luck.