Core2 duo is socket 775. Core i3 is socket 1156. so you will have to choose. You can't upgrade from core2 duo to i3. The H55 1156 boards have come down in price; some are around $75. Be sure to get the H series if you need onboard video, and the cpu supports it. Some i5 or i7 cpus don't have the graphics onboard.
Will need your vender to give you some options. I use a biostar th55b hd micro atx board with 4 dimm slots and some overclocking options. It doesn't have usb 3.0 or sata 6.0 like some of the newer boards, but it works ok. Frys.com had an msi h55 board the other day for only $45 after rebate, but sold out online. It's still available in some of their stores.