Questions about my motherboard

upgrade my processor, or upgrade my motherboard and processor?

Upgrading only the CPU is not really an option, since the new CPU's are different socket than the LGA775 so your current motherboard wont support them anyway.

Yep, upgrading only CPU is a waste of money. Get LGA 1150 and any i5.

Minimum specifications:
OS: Windows 8.1 64 Bit, Windows 8 64 Bit, Windows 7 64 Bit Service Pack 1, Windows Vista 64 Bit Service Pack 2 (NVIDIA video card recommended if running Vista OS)
Processor: Intel Core 2 Quad CPU Q6600 @ 2.40GHz (4 CPUs) / AMD Phenom 9850 Quad-Core Processor (4 CPUs) @ 2.5GHz
Memory: 4GB
Video Card: NVIDIA 9800 GT 1GB / AMD HD 4870 1GB (DX 10, 10.1, 11)
Sound Card: 100% DirectX 10 compatible
HDD Space: 65GB
DVD Drive

Recommended specifications:
OS: Windows 8.1 64 Bit, Windows 8 64 Bit, Windows 7 64 Bit Service Pack 1
Processor: Intel Core i5 3470 @ 3.2GHZ (4 CPUs) / AMD X8 FX-8350 @ 4GHZ (8 CPUs)
Memory: 8GB
Video Card: NVIDIA GTX 660 2GB / AMD HD7870 2GB
Sound Card: 100% DirectX 10 compatible
HDD Space: 65GB
DVD Drive

Your CPU might run it though R* does suggest at least a Quad

though it should not cost much to find a Quad on ebay that should work and your GPU should be fine though i would not expect much more then low settings.

Sometimes though specs can be way off i have seen where people ran games below min just fine and where some have shot well above recommended specs and struggle to run the game.i am just saying you never know for sure until the game drops.

I checked Ebay and Quads are running around 50-70 bucks

That would be your cheapest and easiest way to upgrade to meet the min specs.

If you have the budget i would also upgrade the video card as a Quad can still run a lot of games just fine it really depends on what you want out of it this upgrade.

If you also want to play more games coming out it might be best to at the least upgrade the CPU and GPU if you can run all the games you have now at the settings you like but just want to play GTA V it should hold you over but do not expect it ti play newer games as more and more games are needing at least a Quad and a 7850.

if i was you i would upgrade the CPU+MB if you can later upgrade the GPU as getting a newer Intel like an i5 it will bottleneck the GPU and might be over kill if you keep running the older GPU.. And more and more newer games are needing a 7850 to run at around Medium specs.

Upgrading CPU won't make a big difference you should upgrade GPU first and then CPU, and with that socket is not even worth upgrading CPU there, because for a good CPU you need another motherboard, you know games depend more on GPU than CPU right?