|"it's an i3 M370"|
No, it's an i3-370M. The M comes at the end of the model number & identifies it as a mobile processor.
"ill need to upgrade the memory also"
Why? Apparently you have 8GB already.
"I game with it and trying to figure if a processor upgrade would help performance greatly"
While you do need a decent CPU for gaming, performance is more dependant on the GPU (graphics). You can have the fastest CPU available, but if your GPU sucks, your gaming will suck. You never posted the model number of your laptop, but I'll guess that it's the following one (or very similar):
Sorry, but it's not a good gamer due to the Intel HD graphics. Nothing you upgrade is gonna change that. Play your games on low settings with low resolution & save up for a gaming laptop with decent gaming graphics.