Currently my machine has a P8Z77-v Pro with a i5-3570K 3.4GHz and 8 gigs of RAM. I am trying to determine if I could get by with just adding a bit more RAM or if I'd see a pretty drastic improvement if I upgraded my mobo/processor. My two lines of thought currently are to just buy 8 or 16 gigs of DDR3 for my current setup or get a new mobo/processor(ryzen 5 maybe 7)/16 gigs of ram. My video card is a 2070 if that makes any difference. Thanks for any advice.
I would get another 8 gigs of ram to make your total 16. As a best practice you shouldn't settle for anything less, especially if its cheap to get. You didn't specify your power supply, but make sure you double whatever wattage your GPU recommends to power your whole system. Your particular GPU recommends a 550 watt PSU, which means you should have a PSU that can at least give you no less than 1000 watts, if not 1100. I have a 1250 watt PSU, and I probably should have gotten more than that. I'd take your CPU into account as well with that decision.
Others will tell you to go solely by what the GPU recommends, which will probably be around 600-700 watts depending on how high end it is. But a good rule of thumb is to exceed whatever is recommended. A component as important as the PSU is far too important to just get "enough". Other than that, there are websites that will tell you if your computer meets the minimum or recommended specs for a particular game such as the one linked below. It first has to scan your computer before it can tell you anything, its fairly straight forward.
System Requirements Lab - Can you Run it?