Appears to be a Core2Quad system (at best)? Do you have the specific model?
I think the "best" CPU available for it was a Q8300, so hopefully you at least have that. A 1050 would be the max performing card I'd look to pair with it.
Older prebuilts, using OEM motherboards can be a bit problematic with newer GPUs. I think it relates to the UEFI (or lack thereof).
I think the 900 series behaved a little better on older boards, as did the 700 series. I would anticipate a GPU like a 750TI to just be simpler overall, albeit older and a bit lesser of a performer.
I'd expect the PSU to be pretty low powered and, if the system is original from the C2Q era, it's somewhere between 8-10 years old at the point, and I'd suggest replacing*.
*Depending on the motherboard though, the power connectors may be proprietary, making replacing the PSU no simple task.
*EDIT* Assuming your motherboard looks like this:
https://www.ebay.com/i/351957520472?rt=nc
Then those are standard 20/24pin ATX and 4pin EPS, so it'll be easy enough to replace..... assuming the PSU has the same physical ATX dimensions, otherwise you're looking at replacing the case too.