If you have socket AM3, then you will need a discrete graphics card. There are no APU (processors with graphics) made for socket AM3.
AMD ATHLON II & PHENOM II CPUs are all AM3 Socket CPUs. They all are Multicore CPUs.
As for a Graphics card. You can purchase an older cheaper GPU card (AMD or Nvidia) depending on your PSU wattage according to this website: PSU REQUIREMENTS - RealHardTechX
Yes, @neon is correct. There are no AM3 APUs from AMD.
Does your Asus Motherboard itself have integrated Graphics?