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I think what killer was trying to say is that it's not worth it to spend so little money upgrading your system. A used system worth $250 isn't that far in performance from a new system you spend $300 on. The parts might be newer, but they would still be really low end. by saving up more money you'll get that increase in gaming performance you are looking for. I agree. When people come here with $300 and want a gaming machine, I tell them to get an Xbox/PS4. If you only have $300 I suggest the same. You have several problems with your idea. First, I don't think you'll get $250 for that. Here are some systems in my local craigslist.
https://chico.craigslist.org/sys/d/sleeper-pc-stealth-xps-gaming/6251966111.html
Better than yours in every way, only $300. Why should someone spend that much, for a much lower machine?
https://chico.craigslist.org/sys/d/extremely-fast-slim-desktop/6267827561.html
Here is a system similar to yours, but doesn't have the GPU. But this is $125 and someone else can buy or reuse a GPU for the much less then another $125. A used GTX550TI isn't worth $125, more like $25.
I would think something closer to $150 is more what that system was worth. But even if you got $250 for it, and ponied up another $100, $350 doesn't buy you a lot of PC. $100 goes to windows for the OS license, leaving you with $250. Lowest end motherboards with shipping will be another $60. $50 each for a low end CPU and ram? Most of the lowest end parts you are looking at are $50+. At best you'll be able to get 5 of them. There just isn't enough money for a real system with a real gaming GPU.