Looking up that H57 board on newegg shows it to be a LGA1156 board (for the first gen Core-i processors). For SandyBridge processors (second gen Core-i2) you need LGA1155.
I mentioned four different chipsets for LGA1155 boards. In simplistic terms, the new Z68 chipset gives you access to most features, like QuickSync, integrated graphics & K-model overclocking, but is likely to be more expensive. P67 allows K-model overclocking, and is recommended if you rely on an add-in graphics card (like your 4850). H67 has the QuickSync & integrated graphics features already mentioned, but no overclocking; AFAIK H61 is a budget cut-down version of H67 (typically on smaller form-factors).
Lulu's suggestion of "Intel Core i5-2500K + GIGABYTE GA-Z68A-D3H-B3" is a good place to start because it covers most bases. If you need something cheaper, then there are plenty of options at lower price points (e.g. motherboards with fewer features).