The H55 will work. It's an alright cooler but you can do far better for the money. It will do what you're asking of it.
The 8320 is more than 5 years old, and AMD has publicly stated that the FX series were a failure and a mistake. So, if the company that built them are ashamed... Anyway it's equivalent in gaming to the $60 Intel Pentium G4560. Granted, with the Pentium you'd need a new motherboard and RAM, so the FX may still make sense to give a little more life to an aging system.
Regarding your RAM, it will probably play nicely together but that isn't always the case. You won't know until you try.