Best motherboard for i3 2120?

Z77 and Z68 are capable of overclocking, if you want the best results overclocking, you need a K series CPU (unlocked multiplier). ALthough a non-K CPU in the i5 and i7 range (one that has a turbo mode) can still be overclocked, but not as much as a K series.

THe H-series of chipsets do not have the multiplier overclocking ability, and you can't realistically get much out of them overclocking (<5% at the most, via bclk clocking).

If you are going with a core i3, there is no Turbo, so forget about overclocking with that CPU. If in the future, you ever upgrade to an i5 or i7, you might have the itch to overclock, and then you'll thank yourself for investing in a Z77 (or Z68) motherboard. The newer Z or H 7x series of chipsets also support PCI-E gen 3.0 (as do some older 6x series of chipsets, depending on motherboard). That is an important feature if you ever decide to go multi-GPU. On that regard, the H-series of chipsets do not usually allow multi-GPU because the PCI-E 16x lane is not switched into 2 lanes.

Prices of Z7x and H7x series of boards are not too far apart, if you can, invest in a Z77 board and be future-proof (with i5 and i7 overclocking and multi-GPU, if you REALLY want that later on).