The GPU will work. Have no idea what PSU you have, so no idea if and how it will work. In theory, 450watt is enough for such setup. But it comes down to the quality of PSU as this card is somewhere between 150 and 200watt. So a low quality PSU might (and probably will) fail.
Now about RAM - AFAIR, H61 do not support manual RAM configuration and support only DDR3-1066/1333.
I don't know what your budget and what you can get for it, So here are few points for you to consider:
Instead of flashy RAM, it would be better to invest in a better MB to have support for faster RAM. there is up to 15-20% performance boost in going from DDR3-1066 to DDR3-1866 (which can be easily achievable with overclock on DDR3-1600. basically my DDR3-1866 is happily running at 2800MHz) in quite a few games. So ultimately, you might want to get an overclockable i5 with supporting chipset. Or at least the later. Cant imagine there is a big difference in price between H61 and P67/Z68 based motherboards.
Even better idea would be to get one of the following:
1. B75 Q75 Q77 H77 - to be able to overclock the non K CPU by 5-10% using BCLK
2. Z75 Z77 - to have complete control on overclocking.
those boards also come with higher speed memory support and more important with PCIe 3.0 over P67/Z68. That will have better compatibility with newer cards. For example, a GTX 1050Ti which performs similarly to GTX 680 is leaps and bounds above the GTX 560 will cost well under 100$ in a year.
The above will probably cost a bit more, but will serve you much longer while providing better performance and upgrade path.