You can use an H61 board for gaming. The reason people don't recommend it is because the CPU multiplier is locked in the H Chipsets (H61/H67)
However, if you aren't overclocking, there is no real reason not to get an H61 board. You can save some money there, but make sure you read the reviews and get a reliable board.
Also, if you are buying an H61 board, don't waste money on an unlocked CPU. (2500k or 2600k). Save some money and get a locked i5-2400/2500 or i7-2600 (or even an i3-2100 if you are on a tight budget)