When overclocking it is best to move the core up around 5mhz at a time until it becomes unstable when benched (furmark is a good one). Once you have idea how far you can go on stock voltage you can bump the core voltage up a bit and then move the core speed up some more. Memory doesn't seem to OC as well as the core most of the time, so I recommend leaving it as is. This can take some time, if you want, you can speed it up by googling 6770 overclocking to see what others are able to achieve. That will give you some idea of what you can get.
Have a google to see what core clock speeds other people are getting. If there is a 15% - 25% increase above stock clocks then it probably is worth. I would check if those clocks are at the stock core voltage and the stock cooler, they will probably say if it was at stock or what voltage they are at if it wasn't at stock. You can save a bit of time by jumping the clocks up a bit at the start. i.e. my gtx 470 was stock core at 605MHz, most people were getting around 800MHz so I jumped to around 730MHz and started to increase from there.
How decent is you PSU, what is the wattage and brand? I wouldn't start messing if you don't have a decent PSU. Furmark or similar will put under heavy loading more than a game will. Watch your temps!!! Don't allow it to go above 90C in Furmark (to be safe).