Advice needed for gaming PC

Hello
I am in the process of upgrading my PC, I am going to upgrade the motherboard, RAM, and CPU cooler. I have a few parts in mind, and am wondering if all these parts will be compatible with the rest of my system.

Already got:
Phenom II x3 720
Radeon HD 5770
Thermaltake 650w PSU
Seagate 250 GB Hard drive (big enough for what I need it for)
Windows 7 Ultimate

Thinking of getting:
ASUS M4A78L-M motherboard
4GB (2x2) DDR2 800MHz RAM (any brand)
XIGMATEK HDT-S963 CPU cooler

One advantage of that motherboard is that is has Advanced Clock Calibration, so I will try and unlock my x3 720's fourth core, and then maybe a mild overclock too.
Will all these parts be compatible, and will the CPU work with that motherboard straight out of the box without a BIOS update? And will that cooler work on the ASUS motherboard?
Thanks

I would say for a fresh build : go with AM3/DDR3 and any SB710/750 can unlock but ths is not a given , rather a bonus

I dont really like the sound of a fresh build, because the parts that I already have are good enough, and I only play games at 1440x900, so quite low.
I live in the UK, so I cant order anything from Newegg

The Integrated Memory Controller (IMC) on that socket AM3 720BE can 'talk' to both DDR2 and DDR3 so if u need to buy both RAM and motherboard an AM3 socket motherboard sporting DDR3 DIMM slots for RAM and a pair of DDR3 RAMs would be fine When the music's over your DDR3 can be salvaged as the sun has gone down on DDR2 platforms We could help better if u state your budget in pounds too ^^

Would I see a big performance increase in games using DDR3 rather than DDR2?
And my original budget for the motherboard was £50, but I may need to extend it

If you want a newer motherboard with USB3 then you need to budget closer to $100. Down at $50 its limited to smaller, older motherboards they are trying to unload before they become unsellable.

DDR2 RAM is not much cheaper than DDR3. In a couple years if you have a problem, DDR3 RAM will still be easy to replace, but DDR2 may become something you have to pay silly amounts for used on ebay.