Need help with new upgrades

I plan on upgrading my processor because it is pretty old and I'm starting to have trouble running some new games. I do not know whether or not I should or need to upgrade my motherboard. Here are my hardware specs as of right now:

AMD Athlon 64 X2 Dual Core Processor 4600+ 2.41 GHz
2 GB of ram
Nvidia GeForce 880gt 512
ASUS A8N32-SLI Deluxe 939 NVIDIA nForce4

After talking to a computer tech guy, I was told that my ASUS motherboard could work with AM2 processors and that there was no point to upgrade to AM2+ and get a quad core processor because most games still use one or two cores. I was looking at Newegg and I was wondering if I should buy one of the AMD Athlon 64 X2 6000+? I am interested in buying a more effective processor if one is available ,however, this was the only one I could find that looks like it would work good with games.

Newegg.com - AMD Athlon 64 X2 6000+ Windsor 3.0GHz 2 x 1MB L2 Cache Socket AM2 125W Dual-Core Processor - Processors - Desktops
or
Newegg.com - AMD Athlon 64 X2 6000+ 3.1GHz 1MB L2 Cache Socket AM2 89W Dual-Core Processor - Processors - Desktops

I also plan on buying two more GBs of ram to help give my computer a boast. I'm not very experienced and my friend initially helped me build my computer. Does my upgrade plan seem like a good idea? Any suggestions or comments about any other upgrades to increase my computers performance? Thanks.