You can't run those cards on that Power supply.
You need to upgrade your power supply.
Plus, it also depends on whether you have a PCI-Express Slot in your motherboard. Most likely you will.
Anyways, if you are upgrading the GPU , you will need to upgrade the Power Supply for sure. 350 Watts just won't cut it.
If you mention a budget for both GPU and PSU, I could tell you.
Btw, the cards your son mentioned, might still bottleneck , depending on what sort of processor you have.
That's something you have to take into consideration.